Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

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Christophe Coupé

2018-04-01

Full Text Available As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM, which address grouping of observations, and generalized linear mixed-effects models (GLMM, which offer a family of distributions for the dependent variable. Generalized additive models (GAM are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS. We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

Science.gov (United States)

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we

Advanced statistics: linear regression, part II: multiple linear regression.

Science.gov (United States)

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Non-linear auto-regressive models for cross-frequency coupling in neural time series

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Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre

2017-01-01

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

Science.gov (United States)

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Non-linear calibration models for near infrared spectroscopy

DEFF Research Database (Denmark)

Ni, Wangdong; Nørgaard, Lars; Mørup, Morten

2014-01-01

by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear...... models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS......-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration...

Applied linear regression

CERN Document Server

Weisberg, Sanford

2013-01-01

Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus

Regression of non-linear coupling of noise in LIGO detectors

Science.gov (United States)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

Science.gov (United States)

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.

Linear regression crash prediction models : issues and proposed solutions.

Science.gov (United States)

2010-05-01

The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...

Linear regression

CERN Document Server

Olive, David J

2017-01-01

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study.

Science.gov (United States)

Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y

2008-02-18

The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.

Identification of Influential Points in a Linear Regression Model

Directory of Open Access Journals (Sweden)

Jan Grosz

2011-03-01

Full Text Available The article deals with the detection and identification of influential points in the linear regression model. Three methods of detection of outliers and leverage points are described. These procedures can also be used for one-sample (independentdatasets. This paper briefly describes theoretical aspects of several robust methods as well. Robust statistics is a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. A simulation model of the simple linear regression is presented.

A test for the parameters of multiple linear regression models ...

African Journals Online (AJOL)

A test for the parameters of multiple linear regression models is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. The test is robust relative to the assumptions of homogeneity of variances and absence of serial correlation of the classical F-test. Under certain null and ...

Recursive Algorithm For Linear Regression

Science.gov (United States)

Varanasi, S. V.

1988-01-01

Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.

The microcomputer scientific software series 2: general linear model--regression.

Science.gov (United States)

Harold M. Rauscher

1983-01-01

The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...

Research on the multiple linear regression in non-invasive blood glucose measurement.

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Zhu, Jianming; Chen, Zhencheng

2015-01-01

A non-invasive blood glucose measurement sensor and the data process algorithm based on the metabolic energy conservation (MEC) method are presented in this paper. The physiological parameters of human fingertip can be measured by various sensing modalities, and blood glucose value can be evaluated with the physiological parameters by the multiple linear regression analysis. Five methods such as enter, remove, forward, backward and stepwise in multiple linear regression were compared, and the backward method had the best performance. The best correlation coefficient was 0.876 with the standard error of the estimate 0.534, and the significance was 0.012 (sig. regression equation was valid. The Clarke error grid analysis was performed to compare the MEC method with the hexokinase method, using 200 data points. The correlation coefficient R was 0.867 and all of the points were located in Zone A and Zone B, which shows the MEC method provides a feasible and valid way for non-invasive blood glucose measurement.

Application of semi-empirical modeling and non-linear regression to unfolding fast neutron spectra from integral reaction rate data

International Nuclear Information System (INIS)

Harker, Y.D.

1976-01-01

A semi-empirical analytical expression representing a fast reactor neutron spectrum has been developed. This expression was used in a non-linear regression computer routine to obtain from measured multiple foil integral reaction data the neutron spectrum inside the Coupled Fast Reactivity Measurement Facility. In this application six parameters in the analytical expression for neutron spectrum were adjusted in the non-linear fitting process to maximize consistency between calculated and measured integral reaction rates for a set of 15 dosimetry detector foils. In two-thirds of the observations the calculated integral agreed with its respective measured value to within the experimental standard deviation, and in all but one case agreement within two standard deviations was obtained. Based on this quality of fit the estimated 70 to 75 percent confidence intervals for the derived spectrum are 10 to 20 percent for the energy range 100 eV to 1 MeV, 10 to 50 percent for 1 MeV to 10 MeV and 50 to 90 percent for 10 MeV to 18 MeV. The analytical model has demonstrated a flexibility to describe salient features of neutron spectra of the fast reactor type. The use of regression analysis with this model has produced a stable method to derive neutron spectra from a limited amount of integral data

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner

Directory of Open Access Journals (Sweden)

Yubo Wang

2017-06-01

Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

Science.gov (United States)

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

Science.gov (United States)

Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

2018-04-01

In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

Direction of Effects in Multiple Linear Regression Models.

Science.gov (United States)

Wiedermann, Wolfgang; von Eye, Alexander

2015-01-01

Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.

OPLS statistical model versus linear regression to assess sonographic predictors of stroke prognosis.

Science.gov (United States)

Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi

2012-01-01

The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.

Evaluating Non-Linear Regression Models in Analysis of Persian Walnut Fruit Growth

Directory of Open Access Journals (Sweden)

I. Karamatlou

2016-02-01

Full Text Available Introduction: Persian walnut (Juglans regia L. is a large, wind-pollinated, monoecious, dichogamous, long lived, perennial tree cultivated for its high quality wood and nuts throughout the temperate regions of the world. Growth model methodology has been widely used in the modeling of plant growth. Mathematical models are important tools to study the plant growth and agricultural systems. These models can be applied for decision-making anddesigning management procedures in horticulture. Through growth analysis, planning for planting systems, fertilization, pruning operations, harvest time as well as obtaining economical yield can be more accessible.Non-linear models are more difficult to specify and estimate than linear models. This research was aimed to studynon-linear regression models based on data obtained from fruit weight, length and width. Selecting the best models which explain that fruit inherent growth pattern of Persian walnut was a further goal of this study. Materials and Methods: The experimental material comprising 14 Persian walnut genotypes propagated by seed collected from a walnut orchard in Golestan province, Minoudasht region, Iran, at latitude 37◦04’N; longitude 55◦32’E; altitude 1060 m, in a silt loam soil type. These genotypes were selected as a representative sampling of the many walnut genotypes available throughout the Northeastern Iran. The age range of walnut trees was 30 to 50 years. The annual mean temperature at the location is16.3◦C, with annual mean rainfall of 690 mm.The data used here is the average of walnut fresh fruit and measured withgram/millimeter/day in2011.According to the data distribution pattern, several equations have been proposed to describesigmoidal growth patterns. Here, we used double-sigmoid and logistic–monomolecular models to evaluate fruit growth based on fruit weight and4different regression models in cluding Richards, Gompertz, Logistic and Exponential growth for evaluation

Discriminative Elastic-Net Regularized Linear Regression.

Science.gov (United States)

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Linear regression in astronomy. II

Science.gov (United States)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Analysis of dental caries using generalized linear and count regression models

Directory of Open Access Journals (Sweden)

Javali M. Phil

2013-11-01

Full Text Available Generalized linear models (GLM are generalization of linear regression models, which allow fitting regression models to response data in all the sciences especially medical and dental sciences that follow a general exponential family. These are flexible and widely used class of such models that can accommodate response variables. Count data are frequently characterized by overdispersion and excess zeros. Zero-inflated count models provide a parsimonious yet powerful way to model this type of situation. Such models assume that the data are a mixture of two separate data generation processes: one generates only zeros, and the other is either a Poisson or a negative binomial data-generating process. Zero inflated count regression models such as the zero-inflated Poisson (ZIP, zero-inflated negative binomial (ZINB regression models have been used to handle dental caries count data with many zeros. We present an evaluation framework to the suitability of applying the GLM, Poisson, NB, ZIP and ZINB to dental caries data set where the count data may exhibit evidence of many zeros and over-dispersion. Estimation of the model parameters using the method of maximum likelihood is provided. Based on the Vuong test statistic and the goodness of fit measure for dental caries data, the NB and ZINB regression models perform better than other count regression models.

(Non) linear regression modelling

NARCIS (Netherlands)

Cizek, P.; Gentle, J.E.; Hardle, W.K.; Mori, Y.

2012-01-01

We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1,…,Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1,…,Xp),p ∈ N, which explain or

Modelling female fertility traits in beef cattle using linear and non-linear models.

Science.gov (United States)

Naya, H; Peñagaricano, F; Urioste, J I

2017-06-01

Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2  linear models; h 2  > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

Science.gov (United States)

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

Characteristics and Properties of a Simple Linear Regression Model

Directory of Open Access Journals (Sweden)

Kowal Robert

2016-12-01

Full Text Available A simple linear regression model is one of the pillars of classic econometrics. Despite the passage of time, it continues to raise interest both from the theoretical side as well as from the application side. One of the many fundamental questions in the model concerns determining derivative characteristics and studying the properties existing in their scope, referring to the first of these aspects. The literature of the subject provides several classic solutions in that regard. In the paper, a completely new design is proposed, based on the direct application of variance and its properties, resulting from the non-correlation of certain estimators with the mean, within the scope of which some fundamental dependencies of the model characteristics are obtained in a much more compact manner. The apparatus allows for a simple and uniform demonstration of multiple dependencies and fundamental properties in the model, and it does it in an intuitive manner. The results were obtained in a classic, traditional area, where everything, as it might seem, has already been thoroughly studied and discovered.

Non-linear finite element modeling

DEFF Research Database (Denmark)

Mikkelsen, Lars Pilgaard

The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

Predicting recycling behaviour: Comparison of a linear regression model and a fuzzy logic model.

Science.gov (United States)

Vesely, Stepan; Klöckner, Christian A; Dohnal, Mirko

2016-03-01

In this paper we demonstrate that fuzzy logic can provide a better tool for predicting recycling behaviour than the customarily used linear regression. To show this, we take a set of empirical data on recycling behaviour (N=664), which we randomly divide into two halves. The first half is used to estimate a linear regression model of recycling behaviour, and to develop a fuzzy logic model of recycling behaviour. As the first comparison, the fit of both models to the data included in estimation of the models (N=332) is evaluated. As the second comparison, predictive accuracy of both models for "new" cases (hold-out data not included in building the models, N=332) is assessed. In both cases, the fuzzy logic model significantly outperforms the regression model in terms of fit. To conclude, when accurate predictions of recycling and possibly other environmental behaviours are needed, fuzzy logic modelling seems to be a promising technique. Copyright © 2015 Elsevier Ltd. All rights reserved.

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Directory of Open Access Journals (Sweden)

MC. Souza

Full Text Available Leaf area estimation is an important biometrical trait for evaluating leaf development and plant growth in field and pot experiments. We developed a non-destructive model to estimate the leaf area (LA of Vernonia ferruginea using the length (L and width (W leaf dimensions. Different combinations of linear equations were obtained from L, L2, W, W2, LW and L2W2. The linear regressions using the product of LW dimensions were more efficient to estimate the LA of V. ferruginea than models based on a single dimension (L, W, L2 or W2. Therefore, the linear regression “LA=0.463+0.676WL” provided the most accurate estimate of V. ferruginea leaf area. Validation of the selected model showed that the correlation between real measured leaf area and estimated leaf area was very high.

The Relationship between Economic Growth and Money Laundering – a Linear Regression Model

Directory of Open Access Journals (Sweden)

Daniel Rece

2009-09-01

Full Text Available This study provides an overview of the relationship between economic growth and money laundering modeled by a least squares function. The report analyzes statistically data collected from USA, Russia, Romania and other eleven European countries, rendering a linear regression model. The study illustrates that 23.7% of the total variance in the regressand (level of money laundering is “explained” by the linear regression model. In our opinion, this model will provide critical auxiliary judgment and decision support for anti-money laundering service systems.

Linear and evolutionary polynomial regression models to forecast coastal dynamics: Comparison and reliability assessment

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Bruno, Delia Evelina; Barca, Emanuele; Goncalves, Rodrigo Mikosz; de Araujo Queiroz, Heithor Alexandre; Berardi, Luigi; Passarella, Giuseppe

2018-01-01

In this paper, the Evolutionary Polynomial Regression data modelling strategy has been applied to study small scale, short-term coastal morphodynamics, given its capability for treating a wide database of known information, non-linearly. Simple linear and multilinear regression models were also applied to achieve a balance between the computational load and reliability of estimations of the three models. In fact, even though it is easy to imagine that the more complex the model, the more the prediction improves, sometimes a "slight" worsening of estimations can be accepted in exchange for the time saved in data organization and computational load. The models' outcomes were validated through a detailed statistical, error analysis, which revealed a slightly better estimation of the polynomial model with respect to the multilinear model, as expected. On the other hand, even though the data organization was identical for the two models, the multilinear one required a simpler simulation setting and a faster run time. Finally, the most reliable evolutionary polynomial regression model was used in order to make some conjecture about the uncertainty increase with the extension of extrapolation time of the estimation. The overlapping rate between the confidence band of the mean of the known coast position and the prediction band of the estimated position can be a good index of the weakness in producing reliable estimations when the extrapolation time increases too much. The proposed models and tests have been applied to a coastal sector located nearby Torre Colimena in the Apulia region, south Italy.

Significance tests to determine the direction of effects in linear regression models.

Science.gov (United States)

Wiedermann, Wolfgang; Hagmann, Michael; von Eye, Alexander

2015-02-01

Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non-normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one-sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice. © 2014 The British Psychological Society.

Linear regression metamodeling as a tool to summarize and present simulation model results.

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Jalal, Hawre; Dowd, Bryan; Sainfort, François; Kuntz, Karen M

2013-10-01

Modelers lack a tool to systematically and clearly present complex model results, including those from sensitivity analyses. The objective was to propose linear regression metamodeling as a tool to increase transparency of decision analytic models and better communicate their results. We used a simplified cancer cure model to demonstrate our approach. The model computed the lifetime cost and benefit of 3 treatment options for cancer patients. We simulated 10,000 cohorts in a probabilistic sensitivity analysis (PSA) and regressed the model outcomes on the standardized input parameter values in a set of regression analyses. We used the regression coefficients to describe measures of sensitivity analyses, including threshold and parameter sensitivity analyses. We also compared the results of the PSA to deterministic full-factorial and one-factor-at-a-time designs. The regression intercept represented the estimated base-case outcome, and the other coefficients described the relative parameter uncertainty in the model. We defined simple relationships that compute the average and incremental net benefit of each intervention. Metamodeling produced outputs similar to traditional deterministic 1-way or 2-way sensitivity analyses but was more reliable since it used all parameter values. Linear regression metamodeling is a simple, yet powerful, tool that can assist modelers in communicating model characteristics and sensitivity analyses.

Weighted functional linear regression models for gene-based association analysis.

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Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I

2018-01-01

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

Piecewise linear regression splines with hyperbolic covariates

International Nuclear Information System (INIS)

Cologne, John B.; Sposto, Richard

1992-09-01

Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)

A primer for biomedical scientists on how to execute model II linear regression analysis.

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Ludbrook, John

2012-04-01

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

Modeling the frequency of opposing left-turn conflicts at signalized intersections using generalized linear regression models.

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Zhang, Xin; Liu, Pan; Chen, Yuguang; Bai, Lu; Wang, Wei

2014-01-01

The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation.

Linear Regression on Sparse Features for Single-Channel Speech Separation

DEFF Research Database (Denmark)

Schmidt, Mikkel N.; Olsson, Rasmus Kongsgaard

2007-01-01

In this work we address the problem of separating multiple speakers from a single microphone recording. We formulate a linear regression model for estimating each speaker based on features derived from the mixture. The employed feature representation is a sparse, non-negative encoding of the speech...... mixture in terms of pre-learned speaker-dependent dictionaries. Previous work has shown that this feature representation by itself provides some degree of separation. We show that the performance is significantly improved when regression analysis is performed on the sparse, non-negative features, both...

LINEAR REGRESSION MODEL ESTİMATİON FOR RIGHT CENSORED DATA

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Ersin Yılmaz

2016-05-01

Full Text Available In this study, firstly we will define a right censored data. If we say shortly right-censored data is censoring values that above the exact line. This may be related with scaling device. And then  we will use response variable acquainted from right-censored explanatory variables. Then the linear regression model will be estimated. For censored data’s existence, Kaplan-Meier weights will be used for  the estimation of the model. With the weights regression model  will be consistent and unbiased with that.   And also there is a method for the censored data that is a semi parametric regression and this method also give  useful results  for censored data too. This study also might be useful for the health studies because of the censored data used in medical issues generally.

Evaluation of a multiple linear regression model and SARIMA model in forecasting heat demand for district heating system

International Nuclear Information System (INIS)

Fang, Tingting; Lahdelma, Risto

2016-01-01

Highlights: • Social factor is considered for the linear regression models besides weather file. • Simultaneously optimize all the coefficients for linear regression models. • SARIMA combined with linear regression is used to forecast the heat demand. • The accuracy for both linear regression and time series models are evaluated. - Abstract: Forecasting heat demand is necessary for production and operation planning of district heating (DH) systems. In this study we first propose a simple regression model where the hourly outdoor temperature and wind speed forecast the heat demand. Weekly rhythm of heat consumption as a social component is added to the model to significantly improve the accuracy. The other type of model is the seasonal autoregressive integrated moving average (SARIMA) model with exogenous variables as a combination to take weather factors, and the historical heat consumption data as depending variables. One outstanding advantage of the model is that it peruses the high accuracy for both long-term and short-term forecast by considering both exogenous factors and time series. The forecasting performance of both linear regression models and time series model are evaluated based on real-life heat demand data for the city of Espoo in Finland by out-of-sample tests for the last 20 full weeks of the year. The results indicate that the proposed linear regression model (T168h) using 168-h demand pattern with midweek holidays classified as Saturdays or Sundays gives the highest accuracy and strong robustness among all the tested models based on the tested forecasting horizon and corresponding data. Considering the parsimony of the input, the ease of use and the high accuracy, the proposed T168h model is the best in practice. The heat demand forecasting model can also be developed for individual buildings if automated meter reading customer measurements are available. This would allow forecasting the heat demand based on more accurate heat consumption

Post-processing through linear regression

Science.gov (United States)

van Schaeybroeck, B.; Vannitsem, S.

2011-03-01

Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

Multivariate Linear Regression and CART Regression Analysis of TBM Performance at Abu Hamour Phase-I Tunnel

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Jakubowski, J.; Stypulkowski, J. B.; Bernardeau, F. G.

2017-12-01

The first phase of the Abu Hamour drainage and storm tunnel was completed in early 2017. The 9.5 km long, 3.7 m diameter tunnel was excavated with two Earth Pressure Balance (EPB) Tunnel Boring Machines from Herrenknecht. TBM operation processes were monitored and recorded by Data Acquisition and Evaluation System. The authors coupled collected TBM drive data with available information on rock mass properties, cleansed, completed with secondary variables and aggregated by weeks and shifts. Correlations and descriptive statistics charts were examined. Multivariate Linear Regression and CART regression tree models linking TBM penetration rate (PR), penetration per revolution (PPR) and field penetration index (FPI) with TBM operational and geotechnical characteristics were performed for the conditions of the weak/soft rock of Doha. Both regression methods are interpretable and the data were screened with different computational approaches allowing enriched insight. The primary goal of the analysis was to investigate empirical relations between multiple explanatory and responding variables, to search for best subsets of explanatory variables and to evaluate the strength of linear and non-linear relations. For each of the penetration indices, a predictive model coupling both regression methods was built and validated. The resultant models appeared to be stronger than constituent ones and indicated an opportunity for more accurate and robust TBM performance predictions.

Controlling attribute effect in linear regression

KAUST Repository

Calders, Toon; Karim, Asim A.; Kamiran, Faisal; Ali, Wasif Mohammad; Zhang, Xiangliang

2013-01-01

In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

Controlling attribute effect in linear regression

KAUST Repository

Calders, Toon

2013-12-01

In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

Science.gov (United States)

Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

2016-04-01

Existing evidence suggests that ambient ultrafine particles (UFPs) (regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

QSAR models for prediction study of HIV protease inhibitors using support vector machines, neural networks and multiple linear regression

Directory of Open Access Journals (Sweden)

Rachid Darnag

2017-02-01

Full Text Available Support vector machines (SVM represent one of the most promising Machine Learning (ML tools that can be applied to develop a predictive quantitative structure–activity relationship (QSAR models using molecular descriptors. Multiple linear regression (MLR and artificial neural networks (ANNs were also utilized to construct quantitative linear and non linear models to compare with the results obtained by SVM. The prediction results are in good agreement with the experimental value of HIV activity; also, the results reveal the superiority of the SVM over MLR and ANN model. The contribution of each descriptor to the structure–activity relationships was evaluated.

Biochemical methane potential prediction of plant biomasses: Comparing chemical composition versus near infrared methods and linear versus non-linear models.

Science.gov (United States)

Godin, Bruno; Mayer, Frédéric; Agneessens, Richard; Gerin, Patrick; Dardenne, Pierre; Delfosse, Philippe; Delcarte, Jérôme

2015-01-01

The reliability of different models to predict the biochemical methane potential (BMP) of various plant biomasses using a multispecies dataset was compared. The most reliable prediction models of the BMP were those based on the near infrared (NIR) spectrum compared to those based on the chemical composition. The NIR predictions of local (specific regression and non-linear) models were able to estimate quantitatively, rapidly, cheaply and easily the BMP. Such a model could be further used for biomethanation plant management and optimization. The predictions of non-linear models were more reliable compared to those of linear models. The presentation form (green-dried, silage-dried and silage-wet form) of biomasses to the NIR spectrometer did not influence the performances of the NIR prediction models. The accuracy of the BMP method should be improved to enhance further the BMP prediction models. Copyright © 2014 Elsevier Ltd. All rights reserved.

Post-processing through linear regression

Directory of Open Access Journals (Sweden)

B. Van Schaeybroeck

2011-03-01

Full Text Available Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS method, a new time-dependent Tikhonov regularization (TDTR method, the total least-square method, a new geometric-mean regression (GM, a recently introduced error-in-variables (EVMOS method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified.

These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise. At long lead times the regression schemes (EVMOS, TDTR which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

Method validation using weighted linear regression models for quantification of UV filters in water samples.

Science.gov (United States)

da Silva, Claudia Pereira; Emídio, Elissandro Soares; de Marchi, Mary Rosa Rodrigues

2015-01-01

This paper describes the validation of a method consisting of solid-phase extraction followed by gas chromatography-tandem mass spectrometry for the analysis of the ultraviolet (UV) filters benzophenone-3, ethylhexyl salicylate, ethylhexyl methoxycinnamate and octocrylene. The method validation criteria included evaluation of selectivity, analytical curve, trueness, precision, limits of detection and limits of quantification. The non-weighted linear regression model has traditionally been used for calibration, but it is not necessarily the optimal model in all cases. Because the assumption of homoscedasticity was not met for the analytical data in this work, a weighted least squares linear regression was used for the calibration method. The evaluated analytical parameters were satisfactory for the analytes and showed recoveries at four fortification levels between 62% and 107%, with relative standard deviations less than 14%. The detection limits ranged from 7.6 to 24.1 ng L(-1). The proposed method was used to determine the amount of UV filters in water samples from water treatment plants in Araraquara and Jau in São Paulo, Brazil. Copyright © 2014 Elsevier B.V. All rights reserved.

Electricity consumption forecasting in Italy using linear regression models

Energy Technology Data Exchange (ETDEWEB)

Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio [DIAM, Seconda Universita degli Studi di Napoli, Via Roma 29, 81031 Aversa (CE) (Italy)

2009-09-15

The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of {+-}1% for the best case and {+-}11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)

Electricity consumption forecasting in Italy using linear regression models

International Nuclear Information System (INIS)

Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio

2009-01-01

The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of ±1% for the best case and ±11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)

Comparison of linear and non-linear models for predicting energy expenditure from raw accelerometer data.

Science.gov (United States)

Montoye, Alexander H K; Begum, Munni; Henning, Zachary; Pfeiffer, Karin A

2017-02-01

This study had three purposes, all related to evaluating energy expenditure (EE) prediction accuracy from body-worn accelerometers: (1) compare linear regression to linear mixed models, (2) compare linear models to artificial neural network models, and (3) compare accuracy of accelerometers placed on the hip, thigh, and wrists. Forty individuals performed 13 activities in a 90 min semi-structured, laboratory-based protocol. Participants wore accelerometers on the right hip, right thigh, and both wrists and a portable metabolic analyzer (EE criterion). Four EE prediction models were developed for each accelerometer: linear regression, linear mixed, and two ANN models. EE prediction accuracy was assessed using correlations, root mean square error (RMSE), and bias and was compared across models and accelerometers using repeated-measures analysis of variance. For all accelerometer placements, there were no significant differences for correlations or RMSE between linear regression and linear mixed models (correlations: r  =  0.71-0.88, RMSE: 1.11-1.61 METs; p  >  0.05). For the thigh-worn accelerometer, there were no differences in correlations or RMSE between linear and ANN models (ANN-correlations: r  =  0.89, RMSE: 1.07-1.08 METs. Linear models-correlations: r  =  0.88, RMSE: 1.10-1.11 METs; p  >  0.05). Conversely, one ANN had higher correlations and lower RMSE than both linear models for the hip (ANN-correlation: r  =  0.88, RMSE: 1.12 METs. Linear models-correlations: r  =  0.86, RMSE: 1.18-1.19 METs; p  linear models for the wrist-worn accelerometers (ANN-correlations: r  =  0.82-0.84, RMSE: 1.26-1.32 METs. Linear models-correlations: r  =  0.71-0.73, RMSE: 1.55-1.61 METs; p  models offer a significant improvement in EE prediction accuracy over linear models. Conversely, linear models showed similar EE prediction accuracy to machine learning models for hip- and thigh

Heterotic sigma models and non-linear strings

International Nuclear Information System (INIS)

Hull, C.M.

1986-01-01

The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)

A method for fitting regression splines with varying polynomial order in the linear mixed model.

Science.gov (United States)

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

Modeling Pan Evaporation for Kuwait by Multiple Linear Regression

Science.gov (United States)

Almedeij, Jaber

2012-01-01

Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984

truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models

Directory of Open Access Journals (Sweden)

Maria Karlsson

2014-05-01

Full Text Available Problems with truncated data occur in many areas, complicating estimation and inference. Regarding linear regression models, the ordinary least squares estimator is inconsistent and biased for these types of data and is therefore unsuitable for use. Alternative estimators, designed for the estimation of truncated regression models, have been developed. This paper presents the R package truncSP. The package contains functions for the estimation of semi-parametric truncated linear regression models using three different estimators: the symmetrically trimmed least squares, quadratic mode, and left truncated estimators, all of which have been shown to have good asymptotic and ?nite sample properties. The package also provides functions for the analysis of the estimated models. Data from the environmental sciences are used to illustrate the functions in the package.

EPMLR: sequence-based linear B-cell epitope prediction method using multiple linear regression.

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Lian, Yao; Ge, Meng; Pan, Xian-Ming

2014-12-19

B-cell epitopes have been studied extensively due to their immunological applications, such as peptide-based vaccine development, antibody production, and disease diagnosis and therapy. Despite several decades of research, the accurate prediction of linear B-cell epitopes has remained a challenging task. In this work, based on the antigen's primary sequence information, a novel linear B-cell epitope prediction model was developed using the multiple linear regression (MLR). A 10-fold cross-validation test on a large non-redundant dataset was performed to evaluate the performance of our model. To alleviate the problem caused by the noise of negative dataset, 300 experiments utilizing 300 sub-datasets were performed. We achieved overall sensitivity of 81.8%, precision of 64.1% and area under the receiver operating characteristic curve (AUC) of 0.728. We have presented a reliable method for the identification of linear B cell epitope using antigen's primary sequence information. Moreover, a web server EPMLR has been developed for linear B-cell epitope prediction: http://www.bioinfo.tsinghua.edu.cn/epitope/EPMLR/ .

Estimating monotonic rates from biological data using local linear regression.

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Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

Evaluation of accuracy of linear regression models in predicting urban stormwater discharge characteristics.

Science.gov (United States)

Madarang, Krish J; Kang, Joo-Hyon

2014-06-01

Stormwater runoff has been identified as a source of pollution for the environment, especially for receiving waters. In order to quantify and manage the impacts of stormwater runoff on the environment, predictive models and mathematical models have been developed. Predictive tools such as regression models have been widely used to predict stormwater discharge characteristics. Storm event characteristics, such as antecedent dry days (ADD), have been related to response variables, such as pollutant loads and concentrations. However it has been a controversial issue among many studies to consider ADD as an important variable in predicting stormwater discharge characteristics. In this study, we examined the accuracy of general linear regression models in predicting discharge characteristics of roadway runoff. A total of 17 storm events were monitored in two highway segments, located in Gwangju, Korea. Data from the monitoring were used to calibrate United States Environmental Protection Agency's Storm Water Management Model (SWMM). The calibrated SWMM was simulated for 55 storm events, and the results of total suspended solid (TSS) discharge loads and event mean concentrations (EMC) were extracted. From these data, linear regression models were developed. R(2) and p-values of the regression of ADD for both TSS loads and EMCs were investigated. Results showed that pollutant loads were better predicted than pollutant EMC in the multiple regression models. Regression may not provide the true effect of site-specific characteristics, due to uncertainty in the data. Copyright © 2014 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Linear and non-linear autoregressive models for short-term wind speed forecasting

International Nuclear Information System (INIS)

Lydia, M.; Suresh Kumar, S.; Immanuel Selvakumar, A.; Edwin Prem Kumar, G.

2016-01-01

Highlights: • Models for wind speed prediction at 10-min intervals up to 1 h built on time-series wind speed data. • Four different multivariate models for wind speed built based on exogenous variables. • Non-linear models built using three data mining algorithms outperform the linear models. • Autoregressive models based on wind direction perform better than other models. - Abstract: Wind speed forecasting aids in estimating the energy produced from wind farms. The soaring energy demands of the world and minimal availability of conventional energy sources have significantly increased the role of non-conventional sources of energy like solar, wind, etc. Development of models for wind speed forecasting with higher reliability and greater accuracy is the need of the hour. In this paper, models for predicting wind speed at 10-min intervals up to 1 h have been built based on linear and non-linear autoregressive moving average models with and without external variables. The autoregressive moving average models based on wind direction and annual trends have been built using data obtained from Sotavento Galicia Plc. and autoregressive moving average models based on wind direction, wind shear and temperature have been built on data obtained from Centre for Wind Energy Technology, Chennai, India. While the parameters of the linear models are obtained using the Gauss–Newton algorithm, the non-linear autoregressive models are developed using three different data mining algorithms. The accuracy of the models has been measured using three performance metrics namely, the Mean Absolute Error, Root Mean Squared Error and Mean Absolute Percentage Error.

Predicting Madura cattle growth curve using non-linear model

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Widyas, N.; Prastowo, S.; Widi, T. S. M.; Baliarti, E.

2018-03-01

Madura cattle is Indonesian native. It is a composite breed that has undergone hundreds of years of selection and domestication to reach nowadays remarkable uniformity. Crossbreeding has reached the isle of Madura and the Madrasin, a cross between Madura cows and Limousine semen emerged. This paper aimed to compare the growth curve between Madrasin and one type of pure Madura cows, the common Madura cattle (Madura) using non-linear models. Madura cattles are kept traditionally thus reliable records are hardly available. Data were collected from small holder farmers in Madura. Cows from different age classes (5years) were observed, and body measurements (chest girth, body length and wither height) were taken. In total 63 Madura and 120 Madrasin records obtained. Linear model was built with cattle sub-populations and age as explanatory variables. Body weights were estimated based on the chest girth. Growth curves were built using logistic regression. Results showed that within the same age, Madrasin has significantly larger body compared to Madura (plogistic models fit better for Madura and Madrasin cattle data; with the estimated MSE for these models were 39.09 and 759.28 with prediction accuracy of 99 and 92% for Madura and Madrasin, respectively. Prediction of growth curve using logistic regression model performed well in both types of Madura cattle. However, attempts to administer accurate data on Madura cattle are necessary to better characterize and study these cattle.

Predicting recovery of cognitive function soon after stroke: differential modeling of logarithmic and linear regression.

Science.gov (United States)

Suzuki, Makoto; Sugimura, Yuko; Yamada, Sumio; Omori, Yoshitsugu; Miyamoto, Masaaki; Yamamoto, Jun-ichi

2013-01-01

Cognitive disorders in the acute stage of stroke are common and are important independent predictors of adverse outcome in the long term. Despite the impact of cognitive disorders on both patients and their families, it is still difficult to predict the extent or duration of cognitive impairments. The objective of the present study was, therefore, to provide data on predicting the recovery of cognitive function soon after stroke by differential modeling with logarithmic and linear regression. This study included two rounds of data collection comprising 57 stroke patients enrolled in the first round for the purpose of identifying the time course of cognitive recovery in the early-phase group data, and 43 stroke patients in the second round for the purpose of ensuring that the correlation of the early-phase group data applied to the prediction of each individual's degree of cognitive recovery. In the first round, Mini-Mental State Examination (MMSE) scores were assessed 3 times during hospitalization, and the scores were regressed on the logarithm and linear of time. In the second round, calculations of MMSE scores were made for the first two scoring times after admission to tailor the structures of logarithmic and linear regression formulae to fit an individual's degree of functional recovery. The time course of early-phase recovery for cognitive functions resembled both logarithmic and linear functions. However, MMSE scores sampled at two baseline points based on logarithmic regression modeling could estimate prediction of cognitive recovery more accurately than could linear regression modeling (logarithmic modeling, R(2) = 0.676, PLogarithmic modeling based on MMSE scores could accurately predict the recovery of cognitive function soon after the occurrence of stroke. This logarithmic modeling with mathematical procedures is simple enough to be adopted in daily clinical practice.

Linear regression and the normality assumption.

Science.gov (United States)

Schmidt, Amand F; Finan, Chris

2017-12-16

Researchers often perform arbitrary outcome transformations to fulfill the normality assumption of a linear regression model. This commentary explains and illustrates that in large data settings, such transformations are often unnecessary, and worse may bias model estimates. Linear regression assumptions are illustrated using simulated data and an empirical example on the relation between time since type 2 diabetes diagnosis and glycated hemoglobin levels. Simulation results were evaluated on coverage; i.e., the number of times the 95% confidence interval included the true slope coefficient. Although outcome transformations bias point estimates, violations of the normality assumption in linear regression analyses do not. The normality assumption is necessary to unbiasedly estimate standard errors, and hence confidence intervals and P-values. However, in large sample sizes (e.g., where the number of observations per variable is >10) violations of this normality assumption often do not noticeably impact results. Contrary to this, assumptions on, the parametric model, absence of extreme observations, homoscedasticity, and independency of the errors, remain influential even in large sample size settings. Given that modern healthcare research typically includes thousands of subjects focusing on the normality assumption is often unnecessary, does not guarantee valid results, and worse may bias estimates due to the practice of outcome transformations. Copyright © 2017 Elsevier Inc. All rights reserved.

Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling

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Eric R. Edelman

2017-06-01

Full Text Available For efficient utilization of operating rooms (ORs, accurate schedules of assigned block time and sequences of patient cases need to be made. The quality of these planning tools is dependent on the accurate prediction of total procedure time (TPT per case. In this paper, we attempt to improve the accuracy of TPT predictions by using linear regression models based on estimated surgeon-controlled time (eSCT and other variables relevant to TPT. We extracted data from a Dutch benchmarking database of all surgeries performed in six academic hospitals in The Netherlands from 2012 till 2016. The final dataset consisted of 79,983 records, describing 199,772 h of total OR time. Potential predictors of TPT that were included in the subsequent analysis were eSCT, patient age, type of operation, American Society of Anesthesiologists (ASA physical status classification, and type of anesthesia used. First, we computed the predicted TPT based on a previously described fixed ratio model for each record, multiplying eSCT by 1.33. This number is based on the research performed by van Veen-Berkx et al., which showed that 33% of SCT is generally a good approximation of anesthesia-controlled time (ACT. We then systematically tested all possible linear regression models to predict TPT using eSCT in combination with the other available independent variables. In addition, all regression models were again tested without eSCT as a predictor to predict ACT separately (which leads to TPT by adding SCT. TPT was most accurately predicted using a linear regression model based on the independent variables eSCT, type of operation, ASA classification, and type of anesthesia. This model performed significantly better than the fixed ratio model and the method of predicting ACT separately. Making use of these more accurate predictions in planning and sequencing algorithms may enable an increase in utilization of ORs, leading to significant financial and productivity related

Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling.

Science.gov (United States)

Edelman, Eric R; van Kuijk, Sander M J; Hamaekers, Ankie E W; de Korte, Marcel J M; van Merode, Godefridus G; Buhre, Wolfgang F F A

2017-01-01

For efficient utilization of operating rooms (ORs), accurate schedules of assigned block time and sequences of patient cases need to be made. The quality of these planning tools is dependent on the accurate prediction of total procedure time (TPT) per case. In this paper, we attempt to improve the accuracy of TPT predictions by using linear regression models based on estimated surgeon-controlled time (eSCT) and other variables relevant to TPT. We extracted data from a Dutch benchmarking database of all surgeries performed in six academic hospitals in The Netherlands from 2012 till 2016. The final dataset consisted of 79,983 records, describing 199,772 h of total OR time. Potential predictors of TPT that were included in the subsequent analysis were eSCT, patient age, type of operation, American Society of Anesthesiologists (ASA) physical status classification, and type of anesthesia used. First, we computed the predicted TPT based on a previously described fixed ratio model for each record, multiplying eSCT by 1.33. This number is based on the research performed by van Veen-Berkx et al., which showed that 33% of SCT is generally a good approximation of anesthesia-controlled time (ACT). We then systematically tested all possible linear regression models to predict TPT using eSCT in combination with the other available independent variables. In addition, all regression models were again tested without eSCT as a predictor to predict ACT separately (which leads to TPT by adding SCT). TPT was most accurately predicted using a linear regression model based on the independent variables eSCT, type of operation, ASA classification, and type of anesthesia. This model performed significantly better than the fixed ratio model and the method of predicting ACT separately. Making use of these more accurate predictions in planning and sequencing algorithms may enable an increase in utilization of ORs, leading to significant financial and productivity related benefits.

Modeling exposure–lag–response associations with distributed lag non-linear models

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Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and fractional logit regression at recovering average difference measures in a two sample design.

Science.gov (United States)

Meaney, Christopher; Moineddin, Rahim

2014-01-24

In biomedical research, response variables are often encountered which have bounded support on the open unit interval--(0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models. In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided. If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N0 = N1 = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the

Non-linear Growth Models in Mplus and SAS

Science.gov (United States)

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Endogenous glucose production from infancy to adulthood: a non-linear regression model

NARCIS (Netherlands)

Huidekoper, Hidde H.; Ackermans, Mariëtte T.; Ruiter, An F. C.; Sauerwein, Hans P.; Wijburg, Frits A.

2014-01-01

To construct a regression model for endogenous glucose production (EGP) as a function of age, and compare this with glucose supplementation using commonly used dextrose-based saline solutions at fluid maintenance rate in children. A model was constructed based on EGP data, as quantified by

Use of non-linear mixed-effects modelling and regression analysis to predict the number of somatic coliphages by plaque enumeration after 3 hours of incubation.

Science.gov (United States)

Mendez, Javier; Monleon-Getino, Antonio; Jofre, Juan; Lucena, Francisco

2017-10-01

The present study aimed to establish the kinetics of the appearance of coliphage plaques using the double agar layer titration technique to evaluate the feasibility of using traditional coliphage plaque forming unit (PFU) enumeration as a rapid quantification method. Repeated measurements of the appearance of plaques of coliphages titrated according to ISO 10705-2 at different times were analysed using non-linear mixed-effects regression to determine the most suitable model of their appearance kinetics. Although this model is adequate, to simplify its applicability two linear models were developed to predict the numbers of coliphages reliably, using the PFU counts as determined by the ISO after only 3 hours of incubation. One linear model, when the number of plaques detected was between 4 and 26 PFU after 3 hours, had a linear fit of: (1.48 × Counts 3 h + 1.97); and the other, values >26 PFU, had a fit of (1.18 × Counts 3 h + 2.95). If the number of plaques detected was PFU after 3 hours, we recommend incubation for (18 ± 3) hours. The study indicates that the traditional coliphage plating technique has a reasonable potential to provide results in a single working day without the need to invest in additional laboratory equipment.

Use of probabilistic weights to enhance linear regression myoelectric control.

Science.gov (United States)

Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

2015-12-01

Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts' law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p linear regression control. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

Non-stationary hydrologic frequency analysis using B-spline quantile regression

Science.gov (United States)

Nasri, B.; Bouezmarni, T.; St-Hilaire, A.; Ouarda, T. B. M. J.

2017-11-01

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

[Prediction model of health workforce and beds in county hospitals of Hunan by multiple linear regression].

Science.gov (United States)

Ling, Ru; Liu, Jiawang

2011-12-01

To construct prediction model for health workforce and hospital beds in county hospitals of Hunan by multiple linear regression. We surveyed 16 counties in Hunan with stratified random sampling according to uniform questionnaires,and multiple linear regression analysis with 20 quotas selected by literature view was done. Independent variables in the multiple linear regression model on medical personnels in county hospitals included the counties' urban residents' income, crude death rate, medical beds, business occupancy, professional equipment value, the number of devices valued above 10 000 yuan, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, and utilization rate of hospital beds. Independent variables in the multiple linear regression model on county hospital beds included the the population of aged 65 and above in the counties, disposable income of urban residents, medical personnel of medical institutions in county area, business occupancy, the total value of professional equipment, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, utilization rate of hospital beds, and length of hospitalization. The prediction model shows good explanatory and fitting, and may be used for short- and mid-term forecasting.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

Science.gov (United States)

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis

Science.gov (United States)

Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.

2006-01-01

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

A non-linear state space approach to model groundwater fluctuations

NARCIS (Netherlands)

Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.

2006-01-01

A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual

Modeling Non-Linear Material Properties in Composite Materials

Science.gov (United States)

2016-06-28

Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions

Applicability of linear and non-linear potential flow models on a Wavestar float

DEFF Research Database (Denmark)

Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

2017-01-01

as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...

Using the classical linear regression model in analysis of the dependences of conveyor belt life

Directory of Open Access Journals (Sweden)

Miriam Andrejiová

2013-12-01

Full Text Available The paper deals with the classical linear regression model of the dependence of conveyor belt life on some selected parameters: thickness of paint layer, width and length of the belt, conveyor speed and quantity of transported material. The first part of the article is about regression model design, point and interval estimation of parameters, verification of statistical significance of the model, and about the parameters of the proposed regression model. The second part of the article deals with identification of influential and extreme values that can have an impact on estimation of regression model parameters. The third part focuses on assumptions of the classical regression model, i.e. on verification of independence assumptions, normality and homoscedasticity of residuals.

Augmenting Data with Published Results in Bayesian Linear Regression

Science.gov (United States)

de Leeuw, Christiaan; Klugkist, Irene

2012-01-01

In most research, linear regression analyses are performed without taking into account published results (i.e., reported summary statistics) of similar previous studies. Although the prior density in Bayesian linear regression could accommodate such prior knowledge, formal models for doing so are absent from the literature. The goal of this…

Modelling Loudspeaker Non-Linearities

DEFF Research Database (Denmark)

Agerkvist, Finn T.

2007-01-01

This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...

SPLINE LINEAR REGRESSION USED FOR EVALUATING FINANCIAL ASSETS 1

Directory of Open Access Journals (Sweden)

Liviu GEAMBAŞU

2010-12-01

Full Text Available One of the most important preoccupations of financial markets participants was and still is the problem of determining more precise the trend of financial assets prices. For solving this problem there were written many scientific papers and were developed many mathematical and statistical models in order to better determine the financial assets price trend. If until recently the simple linear models were largely used due to their facile utilization, the financial crises that affected the world economy starting with 2008 highlight the necessity of adapting the mathematical models to variation of economy. A simple to use model but adapted to economic life realities is the spline linear regression. This type of regression keeps the continuity of regression function, but split the studied data in intervals with homogenous characteristics. The characteristics of each interval are highlighted and also the evolution of market over all the intervals, resulting reduced standard errors. The first objective of the article is the theoretical presentation of the spline linear regression, also referring to scientific national and international papers related to this subject. The second objective is applying the theoretical model to data from the Bucharest Stock Exchange

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

Science.gov (United States)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

Science.gov (United States)

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

Science.gov (United States)

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-03-26

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

SOME STATISTICAL ISSUES RELATED TO MULTIPLE LINEAR REGRESSION MODELING OF BEACH BACTERIA CONCENTRATIONS

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As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...

Preisach hysteresis model for non-linear 2D heat diffusion

International Nuclear Information System (INIS)

Jancskar, Ildiko; Ivanyi, Amalia

2006-01-01

This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way

Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: Comparison of various error functions

International Nuclear Information System (INIS)

Kumar, K. Vasanth; Porkodi, K.; Rocha, F.

2008-01-01

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r 2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r 2 ), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r 2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K 2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm

Linear Multivariable Regression Models for Prediction of Eddy Dissipation Rate from Available Meteorological Data

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MCKissick, Burnell T. (Technical Monitor); Plassman, Gerald E.; Mall, Gerald H.; Quagliano, John R.

2005-01-01

Linear multivariable regression models for predicting day and night Eddy Dissipation Rate (EDR) from available meteorological data sources are defined and validated. Model definition is based on a combination of 1997-2000 Dallas/Fort Worth (DFW) data sources, EDR from Aircraft Vortex Spacing System (AVOSS) deployment data, and regression variables primarily from corresponding Automated Surface Observation System (ASOS) data. Model validation is accomplished through EDR predictions on a similar combination of 1994-1995 Memphis (MEM) AVOSS and ASOS data. Model forms include an intercept plus a single term of fixed optimal power for each of these regression variables; 30-minute forward averaged mean and variance of near-surface wind speed and temperature, variance of wind direction, and a discrete cloud cover metric. Distinct day and night models, regressing on EDR and the natural log of EDR respectively, yield best performance and avoid model discontinuity over day/night data boundaries.

Non-linear Loudspeaker Unit Modelling

DEFF Research Database (Denmark)

Pedersen, Bo Rohde; Agerkvist, Finn T.

2008-01-01

Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....

Quantile regression for the statistical analysis of immunological data with many non-detects.

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Eilers, Paul H C; Röder, Esther; Savelkoul, Huub F J; van Wijk, Roy Gerth

2012-07-07

Immunological parameters are hard to measure. A well-known problem is the occurrence of values below the detection limit, the non-detects. Non-detects are a nuisance, because classical statistical analyses, like ANOVA and regression, cannot be applied. The more advanced statistical techniques currently available for the analysis of datasets with non-detects can only be used if a small percentage of the data are non-detects. Quantile regression, a generalization of percentiles to regression models, models the median or higher percentiles and tolerates very high numbers of non-detects. We present a non-technical introduction and illustrate it with an implementation to real data from a clinical trial. We show that by using quantile regression, groups can be compared and that meaningful linear trends can be computed, even if more than half of the data consists of non-detects. Quantile regression is a valuable addition to the statistical methods that can be used for the analysis of immunological datasets with non-detects.

Quantum algorithm for linear regression

Science.gov (United States)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Alpins and thibos vectorial astigmatism analyses: proposal of a linear regression model between methods

Directory of Open Access Journals (Sweden)

Giuliano de Oliveira Freitas

2013-10-01

Full Text Available PURPOSE: To determine linear regression models between Alpins descriptive indices and Thibos astigmatic power vectors (APV, assessing the validity and strength of such correlations. METHODS: This case series prospectively assessed 62 eyes of 31 consecutive cataract patients with preoperative corneal astigmatism between 0.75 and 2.50 diopters in both eyes. Patients were randomly assorted among two phacoemulsification groups: one assigned to receive AcrySof®Toric intraocular lens (IOL in both eyes and another assigned to have AcrySof Natural IOL associated with limbal relaxing incisions, also in both eyes. All patients were reevaluated postoperatively at 6 months, when refractive astigmatism analysis was performed using both Alpins and Thibos methods. The ratio between Thibos postoperative APV and preoperative APV (APVratio and its linear regression to Alpins percentage of success of astigmatic surgery, percentage of astigmatism corrected and percentage of astigmatism reduction at the intended axis were assessed. RESULTS: Significant negative correlation between the ratio of post- and preoperative Thibos APVratio and Alpins percentage of success (%Success was found (Spearman's ρ=-0.93; linear regression is given by the following equation: %Success = (-APVratio + 1.00x100. CONCLUSION: The linear regression we found between APVratio and %Success permits a validated mathematical inference concerning the overall success of astigmatic surgery.

USE OF THE SIMPLE LINEAR REGRESSION MODEL IN MACRO-ECONOMICAL ANALYSES

Directory of Open Access Journals (Sweden)

Constantin ANGHELACHE

2011-10-01

Full Text Available The article presents the fundamental aspects of the linear regression, as a toolbox which can be used in macroeconomic analyses. The article describes the estimation of the parameters, the statistical tests used, the homoscesasticity and heteroskedasticity. The use of econometrics instrument in macroeconomics is an important factor that guarantees the quality of the models, analyses, results and possible interpretation that can be drawn at this level.

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

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Wiedermann, Wolfgang; Artner, Richard; von Eye, Alexander

2017-01-01

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Comparing Regression Coefficients between Nested Linear Models for Clustered Data with Generalized Estimating Equations

Science.gov (United States)

Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer

2013-01-01

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Development of statistical linear regression model for metals from transportation land uses.

Science.gov (United States)

Maniquiz, Marla C; Lee, Soyoung; Lee, Eunju; Kim, Lee-Hyung

2009-01-01

The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

International Nuclear Information System (INIS)

Adcock, T. A. A.; Taylor, P. H.

2016-01-01

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum

Modeling Fire Occurrence at the City Scale: A Comparison between Geographically Weighted Regression and Global Linear Regression.

Science.gov (United States)

Song, Chao; Kwan, Mei-Po; Zhu, Jiping

2017-04-08

An increasing number of fires are occurring with the rapid development of cities, resulting in increased risk for human beings and the environment. This study compares geographically weighted regression-based models, including geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), which integrates spatial and temporal effects and global linear regression models (LM) for modeling fire risk at the city scale. The results show that the road density and the spatial distribution of enterprises have the strongest influences on fire risk, which implies that we should focus on areas where roads and enterprises are densely clustered. In addition, locations with a large number of enterprises have fewer fire ignition records, probably because of strict management and prevention measures. A changing number of significant variables across space indicate that heterogeneity mainly exists in the northern and eastern rural and suburban areas of Hefei city, where human-related facilities or road construction are only clustered in the city sub-centers. GTWR can capture small changes in the spatiotemporal heterogeneity of the variables while GWR and LM cannot. An approach that integrates space and time enables us to better understand the dynamic changes in fire risk. Thus governments can use the results to manage fire safety at the city scale.

Use of multiple linear regression and logistic regression models to investigate changes in birthweight for term singleton infants in Scotland.

Science.gov (United States)

Bonellie, Sandra R

2012-10-01

To illustrate the use of regression and logistic regression models to investigate changes over time in size of babies particularly in relation to social deprivation, age of the mother and smoking. Mean birthweight has been found to be increasing in many countries in recent years, but there are still a group of babies who are born with low birthweights. Population-based retrospective cohort study. Multiple linear regression and logistic regression models are used to analyse data on term 'singleton births' from Scottish hospitals between 1994-2003. Mothers who smoke are shown to give birth to lighter babies on average, a difference of approximately 0.57 Standard deviations lower (95% confidence interval. 0.55-0.58) when adjusted for sex and parity. These mothers are also more likely to have babies that are low birthweight (odds ratio 3.46, 95% confidence interval 3.30-3.63) compared with non-smokers. Low birthweight is 30% more likely where the mother lives in the most deprived areas compared with the least deprived, (odds ratio 1.30, 95% confidence interval 1.21-1.40). Smoking during pregnancy is shown to have a detrimental effect on the size of infants at birth. This effect explains some, though not all, of the observed socioeconomic birthweight. It also explains much of the observed birthweight differences by the age of the mother.   Identifying mothers at greater risk of having a low birthweight baby as important implications for the care and advice this group receives. © 2012 Blackwell Publishing Ltd.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

Science.gov (United States)

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Multiple linear regression and regression with time series error models in forecasting PM10 concentrations in Peninsular Malaysia.

Science.gov (United States)

Ng, Kar Yong; Awang, Norhashidah

2018-01-06

Frequent haze occurrences in Malaysia have made the management of PM 10 (particulate matter with aerodynamic less than 10 μm) pollution a critical task. This requires knowledge on factors associating with PM 10 variation and good forecast of PM 10 concentrations. Hence, this paper demonstrates the prediction of 1-day-ahead daily average PM 10 concentrations based on predictor variables including meteorological parameters and gaseous pollutants. Three different models were built. They were multiple linear regression (MLR) model with lagged predictor variables (MLR1), MLR model with lagged predictor variables and PM 10 concentrations (MLR2) and regression with time series error (RTSE) model. The findings revealed that humidity, temperature, wind speed, wind direction, carbon monoxide and ozone were the main factors explaining the PM 10 variation in Peninsular Malaysia. Comparison among the three models showed that MLR2 model was on a same level with RTSE model in terms of forecasting accuracy, while MLR1 model was the worst.

A Linear Regression Model for Global Solar Radiation on Horizontal Surfaces at Warri, Nigeria

Directory of Open Access Journals (Sweden)

Michael S. Okundamiya

2013-10-01

Full Text Available The growing anxiety on the negative effects of fossil fuels on the environment and the global emission reduction targets call for a more extensive use of renewable energy alternatives. Efficient solar energy utilization is an essential solution to the high atmospheric pollution caused by fossil fuel combustion. Global solar radiation (GSR data, which are useful for the design and evaluation of solar energy conversion system, are not measured at the forty-five meteorological stations in Nigeria. The dearth of the measured solar radiation data calls for accurate estimation. This study proposed a temperature-based linear regression, for predicting the monthly average daily GSR on horizontal surfaces, at Warri (latitude 5.020N and longitude 7.880E an oil city located in the south-south geopolitical zone, in Nigeria. The proposed model is analyzed based on five statistical indicators (coefficient of correlation, coefficient of determination, mean bias error, root mean square error, and t-statistic, and compared with the existing sunshine-based model for the same study. The results indicate that the proposed temperature-based linear regression model could replace the existing sunshine-based model for generating global solar radiation data. Keywords: air temperature; empirical model; global solar radiation; regression analysis; renewable energy; Warri

Use of probabilistic weights to enhance linear regression myoelectric control

Science.gov (United States)

Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.

2015-12-01

Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

Prediction of minimum temperatures in an alpine region by linear and non-linear post-processing of meteorological models

Directory of Open Access Journals (Sweden)

R. Barbiero

2007-05-01

Full Text Available Model Output Statistics (MOS refers to a method of post-processing the direct outputs of numerical weather prediction (NWP models in order to reduce the biases introduced by a coarse horizontal resolution. This technique is especially useful in orographically complex regions, where large differences can be found between the NWP elevation model and the true orography. This study carries out a comparison of linear and non-linear MOS methods, aimed at the prediction of minimum temperatures in a fruit-growing region of the Italian Alps, based on the output of two different NWPs (ECMWF T511–L60 and LAMI-3. Temperature, of course, is a particularly important NWP output; among other roles it drives the local frost forecast, which is of great interest to agriculture. The mechanisms of cold air drainage, a distinctive aspect of mountain environments, are often unsatisfactorily captured by global circulation models. The simplest post-processing technique applied in this work was a correction for the mean bias, assessed at individual model grid points. We also implemented a multivariate linear regression on the output at the grid points surrounding the target area, and two non-linear models based on machine learning techniques: Neural Networks and Random Forest. We compare the performance of all these techniques on four different NWP data sets. Downscaling the temperatures clearly improved the temperature forecasts with respect to the raw NWP output, and also with respect to the basic mean bias correction. Multivariate methods generally yielded better results, but the advantage of using non-linear algorithms was small if not negligible. RF, the best performing method, was implemented on ECMWF prognostic output at 06:00 UTC over the 9 grid points surrounding the target area. Mean absolute errors in the prediction of 2 m temperature at 06:00 UTC were approximately 1.2°C, close to the natural variability inside the area itself.

Convergence diagnostics for Eigenvalue problems with linear regression model

International Nuclear Information System (INIS)

Shi, Bo; Petrovic, Bojan

2011-01-01

Although the Monte Carlo method has been extensively used for criticality/Eigenvalue problems, a reliable, robust, and efficient convergence diagnostics method is still desired. Most methods are based on integral parameters (multiplication factor, entropy) and either condense the local distribution information into a single value (e.g., entropy) or even disregard it. We propose to employ the detailed cycle-by-cycle local flux evolution obtained by using mesh tally mechanism to assess the source and flux convergence. By applying a linear regression model to each individual mesh in a mesh tally for convergence diagnostics, a global convergence criterion can be obtained. We exemplify this method on two problems and obtain promising diagnostics results. (author)

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

INTRODUCTION TO A COMBINED MULTIPLE LINEAR REGRESSION AND ARMA MODELING APPROACH FOR BEACH BACTERIA PREDICTION

Science.gov (United States)

Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...

Testing hypotheses for differences between linear regression lines

Science.gov (United States)

Stanley J. Zarnoch

2009-01-01

Five hypotheses are identified for testing differences between simple linear regression lines. The distinctions between these hypotheses are based on a priori assumptions and illustrated with full and reduced models. The contrast approach is presented as an easy and complete method for testing for overall differences between the regressions and for making pairwise...

Regression and regression analysis time series prediction modeling on climate data of quetta, pakistan

International Nuclear Information System (INIS)

Jafri, Y.Z.; Kamal, L.

2007-01-01

Various statistical techniques was used on five-year data from 1998-2002 of average humidity, rainfall, maximum and minimum temperatures, respectively. The relationships to regression analysis time series (RATS) were developed for determining the overall trend of these climate parameters on the basis of which forecast models can be corrected and modified. We computed the coefficient of determination as a measure of goodness of fit, to our polynomial regression analysis time series (PRATS). The correlation to multiple linear regression (MLR) and multiple linear regression analysis time series (MLRATS) were also developed for deciphering the interdependence of weather parameters. Spearman's rand correlation and Goldfeld-Quandt test were used to check the uniformity or non-uniformity of variances in our fit to polynomial regression (PR). The Breusch-Pagan test was applied to MLR and MLRATS, respectively which yielded homoscedasticity. We also employed Bartlett's test for homogeneity of variances on a five-year data of rainfall and humidity, respectively which showed that the variances in rainfall data were not homogenous while in case of humidity, were homogenous. Our results on regression and regression analysis time series show the best fit to prediction modeling on climatic data of Quetta, Pakistan. (author)

Introduction to statistical modelling 2: categorical variables and interactions in linear regression.

Science.gov (United States)

Lunt, Mark

2015-07-01

In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Correlation and simple linear regression.

Science.gov (United States)

Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

2003-06-01

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Linear regression and sensitivity analysis in nuclear reactor design

International Nuclear Information System (INIS)

Kumar, Akansha; Tsvetkov, Pavel V.; McClarren, Ryan G.

2015-01-01

Highlights: • Presented a benchmark for the applicability of linear regression to complex systems. • Applied linear regression to a nuclear reactor power system. • Performed neutronics, thermal–hydraulics, and energy conversion using Brayton’s cycle for the design of a GCFBR. • Performed detailed sensitivity analysis to a set of parameters in a nuclear reactor power system. • Modeled and developed reactor design using MCNP, regression using R, and thermal–hydraulics in Java. - Abstract: The paper presents a general strategy applicable for sensitivity analysis (SA), and uncertainity quantification analysis (UA) of parameters related to a nuclear reactor design. This work also validates the use of linear regression (LR) for predictive analysis in a nuclear reactor design. The analysis helps to determine the parameters on which a LR model can be fit for predictive analysis. For those parameters, a regression surface is created based on trial data and predictions are made using this surface. A general strategy of SA to determine and identify the influential parameters those affect the operation of the reactor is mentioned. Identification of design parameters and validation of linearity assumption for the application of LR of reactor design based on a set of tests is performed. The testing methods used to determine the behavior of the parameters can be used as a general strategy for UA, and SA of nuclear reactor models, and thermal hydraulics calculations. A design of a gas cooled fast breeder reactor (GCFBR), with thermal–hydraulics, and energy transfer has been used for the demonstration of this method. MCNP6 is used to simulate the GCFBR design, and perform the necessary criticality calculations. Java is used to build and run input samples, and to extract data from the output files of MCNP6, and R is used to perform regression analysis and other multivariate variance, and analysis of the collinearity of data

The regression-calibration method for fitting generalized linear models with additive measurement error

OpenAIRE

James W. Hardin; Henrik Schmeidiche; Raymond J. Carroll

2003-01-01

This paper discusses and illustrates the method of regression calibration. This is a straightforward technique for fitting models with additive measurement error. We present this discussion in terms of generalized linear models (GLMs) following the notation defined in Hardin and Carroll (2003). Discussion will include specified measurement error, measurement error estimated by replicate error-prone proxies, and measurement error estimated by instrumental variables. The discussion focuses on s...

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

Science.gov (United States)

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were

A Non-linear Stochastic Model for an Office Building with Air Infiltration

DEFF Research Database (Denmark)

Thavlov, Anders; Madsen, Henrik

2015-01-01

This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...

Modelling and Predicting Backstroke Start Performance Using Non-Linear and Linear Models.

Science.gov (United States)

de Jesus, Karla; Ayala, Helon V H; de Jesus, Kelly; Coelho, Leandro Dos S; Medeiros, Alexandre I A; Abraldes, José A; Vaz, Mário A P; Fernandes, Ricardo J; Vilas-Boas, João Paulo

2018-03-01

Our aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances.

Straight line fitting and predictions: On a marginal likelihood approach to linear regression and errors-in-variables models

Science.gov (United States)

Christiansen, Bo

2015-04-01

Linear regression methods are without doubt the most used approaches to describe and predict data in the physical sciences. They are often good first order approximations and they are in general easier to apply and interpret than more advanced methods. However, even the properties of univariate regression can lead to debate over the appropriateness of various models as witnessed by the recent discussion about climate reconstruction methods. Before linear regression is applied important choices have to be made regarding the origins of the noise terms and regarding which of the two variables under consideration that should be treated as the independent variable. These decisions are often not easy to make but they may have a considerable impact on the results. We seek to give a unified probabilistic - Bayesian with flat priors - treatment of univariate linear regression and prediction by taking, as starting point, the general errors-in-variables model (Christiansen, J. Clim., 27, 2014-2031, 2014). Other versions of linear regression can be obtained as limits of this model. We derive the likelihood of the model parameters and predictands of the general errors-in-variables model by marginalizing over the nuisance parameters. The resulting likelihood is relatively simple and easy to analyze and calculate. The well known unidentifiability of the errors-in-variables model is manifested as the absence of a well-defined maximum in the likelihood. However, this does not mean that probabilistic inference can not be made; the marginal likelihoods of model parameters and the predictands have, in general, well-defined maxima. We also include a probabilistic version of classical calibration and show how it is related to the errors-in-variables model. The results are illustrated by an example from the coupling between the lower stratosphere and the troposphere in the Northern Hemisphere winter.

Bayesian quantile regression-based partially linear mixed-effects joint models for longitudinal data with multiple features.

Science.gov (United States)

Zhang, Hanze; Huang, Yangxin; Wang, Wei; Chen, Henian; Langland-Orban, Barbara

2017-01-01

In longitudinal AIDS studies, it is of interest to investigate the relationship between HIV viral load and CD4 cell counts, as well as the complicated time effect. Most of common models to analyze such complex longitudinal data are based on mean-regression, which fails to provide efficient estimates due to outliers and/or heavy tails. Quantile regression-based partially linear mixed-effects models, a special case of semiparametric models enjoying benefits of both parametric and nonparametric models, have the flexibility to monitor the viral dynamics nonparametrically and detect the varying CD4 effects parametrically at different quantiles of viral load. Meanwhile, it is critical to consider various data features of repeated measurements, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution. In this research, we first establish a Bayesian joint models that accounts for all these data features simultaneously in the framework of quantile regression-based partially linear mixed-effects models. The proposed models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also conducted to assess the performance of the proposed methods under different scenarios.

Generalised Partially Linear Regression with Misclassified Data and an Application to Labour Market Transitions

DEFF Research Database (Denmark)

Dlugosz, Stephan; Mammen, Enno; Wilke, Ralf

We consider the semiparametric generalised linear regression model which has mainstream empirical models such as the (partially) linear mean regression, logistic and multinomial regression as special cases. As an extension to related literature we allow a misclassified covariate to be interacted...

Statistical approach for selection of regression model during validation of bioanalytical method

Directory of Open Access Journals (Sweden)

Natalija Nakov

2014-06-01

Full Text Available The selection of an adequate regression model is the basis for obtaining accurate and reproducible results during the bionalytical method validation. Given the wide concentration range, frequently present in bioanalytical assays, heteroscedasticity of the data may be expected. Several weighted linear and quadratic regression models were evaluated during the selection of the adequate curve fit using nonparametric statistical tests: One sample rank test and Wilcoxon signed rank test for two independent groups of samples. The results obtained with One sample rank test could not give statistical justification for the selection of linear vs. quadratic regression models because slight differences between the error (presented through the relative residuals were obtained. Estimation of the significance of the differences in the RR was achieved using Wilcoxon signed rank test, where linear and quadratic regression models were treated as two independent groups. The application of this simple non-parametric statistical test provides statistical confirmation of the choice of an adequate regression model.

Core seismic behaviour: linear and non-linear models

International Nuclear Information System (INIS)

Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.

1981-08-01

The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here

Interpretation of commonly used statistical regression models.

Science.gov (United States)

Kasza, Jessica; Wolfe, Rory

2014-01-01

A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

The number of subjects per variable required in linear regression analyses.

Science.gov (United States)

Austin, Peter C; Steyerberg, Ewout W

2015-06-01

To determine the number of independent variables that can be included in a linear regression model. We used a series of Monte Carlo simulations to examine the impact of the number of subjects per variable (SPV) on the accuracy of estimated regression coefficients and standard errors, on the empirical coverage of estimated confidence intervals, and on the accuracy of the estimated R(2) of the fitted model. A minimum of approximately two SPV tended to result in estimation of regression coefficients with relative bias of less than 10%. Furthermore, with this minimum number of SPV, the standard errors of the regression coefficients were accurately estimated and estimated confidence intervals had approximately the advertised coverage rates. A much higher number of SPV were necessary to minimize bias in estimating the model R(2), although adjusted R(2) estimates behaved well. The bias in estimating the model R(2) statistic was inversely proportional to the magnitude of the proportion of variation explained by the population regression model. Linear regression models require only two SPV for adequate estimation of regression coefficients, standard errors, and confidence intervals. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Evaluation of Linear Regression Simultaneous Myoelectric Control Using Intramuscular EMG.

Science.gov (United States)

Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

2016-04-01

The objective of this study was to evaluate the ability of linear regression models to decode patterns of muscle coactivation from intramuscular electromyogram (EMG) and provide simultaneous myoelectric control of a virtual 3-DOF wrist/hand system. Performance was compared to the simultaneous control of conventional myoelectric prosthesis methods using intramuscular EMG (parallel dual-site control)-an approach that requires users to independently modulate individual muscles in the residual limb, which can be challenging for amputees. Linear regression control was evaluated in eight able-bodied subjects during a virtual Fitts' law task and was compared to performance of eight subjects using parallel dual-site control. An offline analysis also evaluated how different types of training data affected prediction accuracy of linear regression control. The two control systems demonstrated similar overall performance; however, the linear regression method demonstrated improved performance for targets requiring use of all three DOFs, whereas parallel dual-site control demonstrated improved performance for targets that required use of only one DOF. Subjects using linear regression control could more easily activate multiple DOFs simultaneously, but often experienced unintended movements when trying to isolate individual DOFs. Offline analyses also suggested that the method used to train linear regression systems may influence controllability. Linear regression myoelectric control using intramuscular EMG provided an alternative to parallel dual-site control for 3-DOF simultaneous control at the wrist and hand. The two methods demonstrated different strengths in controllability, highlighting the tradeoff between providing simultaneous control and the ability to isolate individual DOFs when desired.

New classical r-matrices from integrable non-linear sigma-models

International Nuclear Information System (INIS)

Laartz, J.; Bordemann, M.; Forger, M.; Schaper, U.

1993-01-01

Non-linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is analyzed and it is shown that their non-ultralocal fundamental Poisson bracket relation is governed by a field dependent non antisymmetric r-matrix obeying a dynamical Yang Baxter equation. The fundamental Poisson bracket relations and the r-matrix are derived explicitly and a new kind of algebra is found that is supposed to replace the classical Yang Baxter algebra governing the canonical structure of ultralocal models. (Author) 9 refs

A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models.

Science.gov (United States)

Casero-Alonso, V; López-Fidalgo, J; Torsney, B

2017-01-01

Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

On concurvity in nonlinear and nonparametric regression models

Directory of Open Access Journals (Sweden)

Sonia Amodio

2014-12-01

Full Text Available When data are affected by multicollinearity in the linear regression framework, then concurvity will be present in fitting a generalized additive model (GAM. The term concurvity describes nonlinear dependencies among the predictor variables. As collinearity results in inflated variance of the estimated regression coefficients in the linear regression model, the result of the presence of concurvity leads to instability of the estimated coefficients in GAMs. Even if the backfitting algorithm will always converge to a solution, in case of concurvity the final solution of the backfitting procedure in fitting a GAM is influenced by the starting functions. While exact concurvity is highly unlikely, approximate concurvity, the analogue of multicollinearity, is of practical concern as it can lead to upwardly biased estimates of the parameters and to underestimation of their standard errors, increasing the risk of committing type I error. We compare the existing approaches to detect concurvity, pointing out their advantages and drawbacks, using simulated and real data sets. As a result, this paper will provide a general criterion to detect concurvity in nonlinear and non parametric regression models.

Bayesian linear regression : different conjugate models and their (in)sensitivity to prior-data conflict

NARCIS (Netherlands)

Walter, G.M.; Augustin, Th.; Kneib, Thomas; Tutz, Gerhard

2010-01-01

The paper is concerned with Bayesian analysis under prior-data conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on

Sphaleron in a non-linear sigma model

International Nuclear Information System (INIS)

Sogo, Kiyoshi; Fujimoto, Yasushi.

1989-08-01

We present an exact classical saddle point solution in a non-linear sigma model. It has a topological charge 1/2 and mediates the vacuum transition. The quantum fluctuations and the transition rate are also examined. (author)

Modified Regression Correlation Coefficient for Poisson Regression Model

Science.gov (United States)

Kaengthong, Nattacha; Domthong, Uthumporn

2017-09-01

This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).

Simple and multiple linear regression: sample size considerations.

Science.gov (United States)

Hanley, James A

2016-11-01

The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright © 2016 Elsevier Inc. All rights reserved.

A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

Science.gov (United States)

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

Finiteness of Ricci flat supersymmetric non-linear sigma-models

International Nuclear Information System (INIS)

Alvarez-Gaume, L.; Ginsparg, P.

1985-01-01

Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.)

Using the fuzzy linear regression method to benchmark the energy efficiency of commercial buildings

International Nuclear Information System (INIS)

Chung, William

2012-01-01

Highlights: ► Fuzzy linear regression method is used for developing benchmarking systems. ► The systems can be used to benchmark energy efficiency of commercial buildings. ► The resulting benchmarking model can be used by public users. ► The resulting benchmarking model can capture the fuzzy nature of input–output data. -- Abstract: Benchmarking systems from a sample of reference buildings need to be developed to conduct benchmarking processes for the energy efficiency of commercial buildings. However, not all benchmarking systems can be adopted by public users (i.e., other non-reference building owners) because of the different methods in developing such systems. An approach for benchmarking the energy efficiency of commercial buildings using statistical regression analysis to normalize other factors, such as management performance, was developed in a previous work. However, the field data given by experts can be regarded as a distribution of possibility. Thus, the previous work may not be adequate to handle such fuzzy input–output data. Consequently, a number of fuzzy structures cannot be fully captured by statistical regression analysis. This present paper proposes the use of fuzzy linear regression analysis to develop a benchmarking process, the resulting model of which can be used by public users. An illustrative example is given as well.

Modelling non-linear effects of dark energy

Science.gov (United States)

Bose, Benjamin; Baldi, Marco; Pourtsidou, Alkistis

2018-04-01

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving w models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter ξ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter σv. To quantify the importance of modelling the interaction, we create mock data sets for varying values of ξ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a ξ=0 modelling, ignoring the interaction. We find the fiducial growth parameter f is generally recovered even for very large values of ξ both at z=0.5 and z=1. The ξ=0 modelling is most biased in its estimation of f for the phantom w=‑1.1 case.

Carbon 13 nuclear magnetic resonance chemical shifts empiric calculations of polymers by multi linear regression and molecular modeling

International Nuclear Information System (INIS)

Da Silva Pinto, P.S.; Eustache, R.P.; Audenaert, M.; Bernassau, J.M.

1996-01-01

This work deals with carbon 13 nuclear magnetic resonance chemical shifts empiric calculations by multi linear regression and molecular modeling. The multi linear regression is indeed one way to obtain an equation able to describe the behaviour of the chemical shift for some molecules which are in the data base (rigid molecules with carbons). The methodology consists of structures describer parameters definition which can be bound to carbon 13 chemical shift known for these molecules. Then, the linear regression is used to determine the equation significant parameters. This one can be extrapolated to molecules which presents some resemblances with those of the data base. (O.L.). 20 refs., 4 figs., 1 tab

The algebra of non-local charges in non-linear sigma models

International Nuclear Information System (INIS)

Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.

1993-07-01

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs

Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

DEFF Research Database (Denmark)

Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik

2004-01-01

The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...

Introduction to generalized linear models

CERN Document Server

Dobson, Annette J

2008-01-01

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...

A non-linear model of economic production processes

Science.gov (United States)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

Non-linear characterisation of the physical model of an ancient masonry bridge

International Nuclear Information System (INIS)

Fragonara, L Zanotti; Ceravolo, R; Matta, E; Quattrone, A; De Stefano, A; Pecorelli, M

2012-01-01

This paper presents the non-linear investigations carried out on a scaled model of a two-span masonry arch bridge. The model has been built in order to study the effect of the central pile settlement due to riverbank erosion. Progressive damage was induced in several steps by applying increasing settlements at the central pier. For each settlement step, harmonic shaker tests were conducted under different excitation levels, this allowing for the non-linear identification of the progressively damaged system. The shaker tests have been performed at resonance with the modal frequency of the structure, which were determined from a previous linear identification. Estimated non-linearity parameters, which result from the systematic application of restoring force based identification algorithms, can corroborate models to be used in the reassessment of existing structures. The method used for non-linear identification allows monitoring the evolution of non-linear parameters or indicators which can be used in damage and safety assessment.

A penalized framework for distributed lag non-linear models.

Science.gov (United States)

Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

2017-09-01

Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Privacy-Preserving Distributed Linear Regression on High-Dimensional Data

Directory of Open Access Journals (Sweden)

Gascón Adrià

2017-10-01

Full Text Available We propose privacy-preserving protocols for computing linear regression models, in the setting where the training dataset is vertically distributed among several parties. Our main contribution is a hybrid multi-party computation protocol that combines Yao’s garbled circuits with tailored protocols for computing inner products. Like many machine learning tasks, building a linear regression model involves solving a system of linear equations. We conduct a comprehensive evaluation and comparison of different techniques for securely performing this task, including a new Conjugate Gradient Descent (CGD algorithm. This algorithm is suitable for secure computation because it uses an efficient fixed-point representation of real numbers while maintaining accuracy and convergence rates comparable to what can be obtained with a classical solution using floating point numbers. Our technique improves on Nikolaenko et al.’s method for privacy-preserving ridge regression (S&P 2013, and can be used as a building block in other analyses. We implement a complete system and demonstrate that our approach is highly scalable, solving data analysis problems with one million records and one hundred features in less than one hour of total running time.

An Investigation of the Fit of Linear Regression Models to Data from an SAT[R] Validity Study. Research Report 2011-3

Science.gov (United States)

Kobrin, Jennifer L.; Sinharay, Sandip; Haberman, Shelby J.; Chajewski, Michael

2011-01-01

This study examined the adequacy of a multiple linear regression model for predicting first-year college grade point average (FYGPA) using SAT[R] scores and high school grade point average (HSGPA). A variety of techniques, both graphical and statistical, were used to examine if it is possible to improve on the linear regression model. The results…

On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

International Nuclear Information System (INIS)

Unkel, Steffen; Belka, Claus; Lauber, Kirsten

2016-01-01

The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

Focused information criterion and model averaging based on weighted composite quantile regression

KAUST Repository

Xu, Ganggang; Wang, Suojin; Huang, Jianhua Z.

2013-01-01

We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non

Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.

Science.gov (United States)

Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J

2016-10-03

Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

Science.gov (United States)

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Renormalization a la BRS of the non-linear σ-model

International Nuclear Information System (INIS)

Blasi, A.; Collina, R.

1987-01-01

We characterize the non-linear O(N+1) σ-model in an arbitrary parametrization with a nihilpotent BRS operator obtained from the symmetry transformation by the use of anticommuting parameters. The identity can be made compatible with the presence of a mass term in the model, so we can analyze its stability and prove that the model is anomaly free. This procedure avoids many problems encountered in the conventional analysis; in particular the introduction of an infinite number of sources coupled to the successive variations of the field is not necessary and the linear O(N) symmetry is respected as a consequence of the identity. The approach may provide useful in discussing the renormalizability of a wider class of models with non-linear symmetries. (orig.)

S-AMP for non-linear observation models

DEFF Research Database (Denmark)

Cakmak, Burak; Winther, Ole; Fleury, Bernard H.

2015-01-01

Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...

A Seemingly Unrelated Poisson Regression Model

OpenAIRE

King, Gary

1989-01-01

This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.

A primer on linear models

CERN Document Server

Monahan, John F

2008-01-01

Preface Examples of the General Linear Model Introduction One-Sample Problem Simple Linear Regression Multiple Regression One-Way ANOVA First Discussion The Two-Way Nested Model Two-Way Crossed Model Analysis of Covariance Autoregression Discussion The Linear Least Squares Problem The Normal Equations The Geometry of Least Squares Reparameterization Gram-Schmidt Orthonormalization Estimability and Least Squares Estimators Assumptions for the Linear Mean Model Confounding, Identifiability, and Estimability Estimability and Least Squares Estimators F

An Introduction to the Hybrid Approach of Neural Networks and the Linear Regression Model : An Illustration in the Hedonic Pricing Model of Building Costs

OpenAIRE

浅野, 美代子; マーコ, ユー K.W.

2007-01-01

This paper introduces the hybrid approach of neural networks and linear regression model proposed by Asano and Tsubaki (2003). Neural networks are often credited with its superiority in data consistency whereas the linear regression model provides simple interpretation of the data enabling researchers to verify their hypotheses. The hybrid approach aims at combing the strengths of these two well-established statistical methods. A step-by-step procedure for performing the hybrid approach is pr...

A simple approach to power and sample size calculations in logistic regression and Cox regression models.

Science.gov (United States)

Vaeth, Michael; Skovlund, Eva

2004-06-15

For a given regression problem it is possible to identify a suitably defined equivalent two-sample problem such that the power or sample size obtained for the two-sample problem also applies to the regression problem. For a standard linear regression model the equivalent two-sample problem is easily identified, but for generalized linear models and for Cox regression models the situation is more complicated. An approximately equivalent two-sample problem may, however, also be identified here. In particular, we show that for logistic regression and Cox regression models the equivalent two-sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged. In a simulation study we examine the validity of this approach to power calculations in logistic regression and Cox regression models. Several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives. For the Cox regression model we consider both constant and non-constant hazard rates. The results show that in general the approach is remarkably accurate even in relatively small samples. Some discrepancies are, however, found in small samples with few events and a highly skewed covariate distribution. Comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors. The method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination. Copyright 2004 John Wiley & Sons, Ltd.

A non-linear dissipative model of magnetism

Czech Academy of Sciences Publication Activity Database

Durand, P.; Paidarová, Ivana

2010-01-01

Roč. 89, č. 6 (2010), s. 67004 ISSN 1286-4854 R&D Projects: GA AV ČR IAA100400501 Institutional research plan: CEZ:AV0Z40400503 Keywords : non-linear dissipative model of magnetism * thermodynamics * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry http://epljournal.edpsciences.org/

Study of the 'non-Abelian' current algebra of a non-linear σ-model

International Nuclear Information System (INIS)

Ghosh, Subir

2006-01-01

A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, hep-th/0501106]. The connection with non-commutative geometry is also established

BFLCRM: A BAYESIAN FUNCTIONAL LINEAR COX REGRESSION MODEL FOR PREDICTING TIME TO CONVERSION TO ALZHEIMER'S DISEASE.

Science.gov (United States)

Lee, Eunjee; Zhu, Hongtu; Kong, Dehan; Wang, Yalin; Giovanello, Kelly Sullivan; Ibrahim, Joseph G

2015-12-01

The aim of this paper is to develop a Bayesian functional linear Cox regression model (BFLCRM) with both functional and scalar covariates. This new development is motivated by establishing the likelihood of conversion to Alzheimer's disease (AD) in 346 patients with mild cognitive impairment (MCI) enrolled in the Alzheimer's Disease Neuroimaging Initiative 1 (ADNI-1) and the early markers of conversion. These 346 MCI patients were followed over 48 months, with 161 MCI participants progressing to AD at 48 months. The functional linear Cox regression model was used to establish that functional covariates including hippocampus surface morphology and scalar covariates including brain MRI volumes, cognitive performance (ADAS-Cog), and APOE status can accurately predict time to onset of AD. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFLCRM.

Data Transformations for Inference with Linear Regression: Clarifications and Recommendations

Science.gov (United States)

Pek, Jolynn; Wong, Octavia; Wong, C. M.

2017-01-01

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

BRGLM, Interactive Linear Regression Analysis by Least Square Fit

International Nuclear Information System (INIS)

Ringland, J.T.; Bohrer, R.E.; Sherman, M.E.

1985-01-01

1 - Description of program or function: BRGLM is an interactive program written to fit general linear regression models by least squares and to provide a variety of statistical diagnostic information about the fit. Stepwise and all-subsets regression can be carried out also. There are facilities for interactive data management (e.g. setting missing value flags, data transformations) and tools for constructing design matrices for the more commonly-used models such as factorials, cubic Splines, and auto-regressions. 2 - Method of solution: The least squares computations are based on the orthogonal (QR) decomposition of the design matrix obtained using the modified Gram-Schmidt algorithm. 3 - Restrictions on the complexity of the problem: The current release of BRGLM allows maxima of 1000 observations, 99 variables, and 3000 words of main memory workspace. For a problem with N observations and P variables, the number of words of main memory storage required is MAX(N*(P+6), N*P+P*P+3*N, and 3*P*P+6*N). Any linear model may be fit although the in-memory workspace will have to be increased for larger problems

Learning a Nonnegative Sparse Graph for Linear Regression.

Science.gov (United States)

Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung

2015-09-01

Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.

Support Vector Regression Model Based on Empirical Mode Decomposition and Auto Regression for Electric Load Forecasting

Directory of Open Access Journals (Sweden)

Hong-Juan Li

2013-04-01

Full Text Available Electric load forecasting is an important issue for a power utility, associated with the management of daily operations such as energy transfer scheduling, unit commitment, and load dispatch. Inspired by strong non-linear learning capability of support vector regression (SVR, this paper presents a SVR model hybridized with the empirical mode decomposition (EMD method and auto regression (AR for electric load forecasting. The electric load data of the New South Wales (Australia market are employed for comparing the forecasting performances of different forecasting models. The results confirm the validity of the idea that the proposed model can simultaneously provide forecasting with good accuracy and interpretability.

Removing Malmquist bias from linear regressions

Science.gov (United States)

Verter, Frances

1993-01-01

Malmquist bias is present in all astronomical surveys where sources are observed above an apparent brightness threshold. Those sources which can be detected at progressively larger distances are progressively more limited to the intrinsically luminous portion of the true distribution. This bias does not distort any of the measurements, but distorts the sample composition. We have developed the first treatment to correct for Malmquist bias in linear regressions of astronomical data. A demonstration of the corrected linear regression that is computed in four steps is presented.

Effective connectivity between superior temporal gyrus and Heschl's gyrus during white noise listening: linear versus non-linear models.

Science.gov (United States)

Hamid, Ka; Yusoff, An; Rahman, Mza; Mohamad, M; Hamid, Aia

2012-04-01

This fMRI study is about modelling the effective connectivity between Heschl's gyrus (HG) and the superior temporal gyrus (STG) in human primary auditory cortices. MATERIALS #ENTITYSTARTX00026; Ten healthy male participants were required to listen to white noise stimuli during functional magnetic resonance imaging (fMRI) scans. Statistical parametric mapping (SPM) was used to generate individual and group brain activation maps. For input region determination, two intrinsic connectivity models comprising bilateral HG and STG were constructed using dynamic causal modelling (DCM). The models were estimated and inferred using DCM while Bayesian Model Selection (BMS) for group studies was used for model comparison and selection. Based on the winning model, six linear and six non-linear causal models were derived and were again estimated, inferred, and compared to obtain a model that best represents the effective connectivity between HG and the STG, balancing accuracy and complexity. Group results indicated significant asymmetrical activation (p(uncorr) Model comparison results showed strong evidence of STG as the input centre. The winning model is preferred by 6 out of 10 participants. The results were supported by BMS results for group studies with the expected posterior probability, r = 0.7830 and exceedance probability, ϕ = 0.9823. One-sample t-tests performed on connection values obtained from the winning model indicated that the valid connections for the winning model are the unidirectional parallel connections from STG to bilateral HG (p model comparison between linear and non-linear models using BMS prefers non-linear connection (r = 0.9160, ϕ = 1.000) from which the connectivity between STG and the ipsi- and contralateral HG is gated by the activity in STG itself. We are able to demonstrate that the effective connectivity between HG and STG while listening to white noise for the respective participants can be explained by a non-linear dynamic causal model with

Modeling and verifying non-linearities in heterodyne displacement interferometry

NARCIS (Netherlands)

Cosijns, S.J.A.G.; Haitjema, H.; Schellekens, P.H.J.

2002-01-01

The non-linearities in a heterodyne laser interferometer system occurring from the phase measurement system of the interferometer andfrom non-ideal polarization effects of the optics are modeled into one analytical expression which includes the initial polarization state ofthe laser source, the

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

Science.gov (United States)

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

Science.gov (United States)

Chacón, Max; Jara, José Luis; Miranda, Rodrigo; Katsogridakis, Emmanuel; Panerai, Ronney B

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Construction of multiple linear regression models using blood biomarkers for selecting against abdominal fat traits in broilers.

Science.gov (United States)

Dong, J Q; Zhang, X Y; Wang, S Z; Jiang, X F; Zhang, K; Ma, G W; Wu, M Q; Li, H; Zhang, H

2018-01-01

Plasma very low-density lipoprotein (VLDL) can be used to select for low body fat or abdominal fat (AF) in broilers, but its correlation with AF is limited. We investigated whether any other biochemical indicator can be used in combination with VLDL for a better selective effect. Nineteen plasma biochemical indicators were measured in male chickens from the Northeast Agricultural University broiler lines divergently selected for AF content (NEAUHLF) in the fed state at 46 and 48 d of age. The average concentration of every parameter for the 2 d was used for statistical analysis. Levels of these 19 plasma biochemical parameters were compared between the lean and fat lines. The phenotypic correlations between these plasma biochemical indicators and AF traits were analyzed. Then, multiple linear regression models were constructed to select the best model used for selecting against AF content. and the heritabilities of plasma indicators contained in the best models were estimated. The results showed that 11 plasma biochemical indicators (triglycerides, total bile acid, total protein, globulin, albumin/globulin, aspartate transaminase, alanine transaminase, gamma-glutamyl transpeptidase, uric acid, creatinine, and VLDL) differed significantly between the lean and fat lines (P linear regression models based on albumin/globulin, VLDL, triglycerides, globulin, total bile acid, and uric acid, had higher R2 (0.73) than the model based only on VLDL (0.21). The plasma parameters included in the best models had moderate heritability estimates (0.21 ≤ h2 ≤ 0.43). These results indicate that these multiple linear regression models can be used to select for lean broiler chickens. © 2017 Poultry Science Association Inc.

Assessing ozone and nitrogen impact on net primary productivity with a Generalised non-Linear Model

International Nuclear Information System (INIS)

De Marco, Alessandra; Screpanti, Augusto; Attorre, Fabio; Proietti, Chiara; Vitale, Marcello

2013-01-01

Some studies suggest that in Europe the majority of forest growth increment can be accounted for N deposition and very little by elevated CO 2 . High ozone (O 3 ) concentrations cause reductions in carbon fixation in native plants by offsetting the effects of elevated CO 2 or N deposition. The cause-effect relationships between primary productivity (NPP) of Quercus cerris, Q. ilex and Fagus sylvatica plant species and climate and pollutants (O 3 and N deposition) in Italy have been investigated by application of Generalised Linear/non-Linear regression model (GLZ model). The GLZ model highlighted: i) cumulative O 3 concentration-based indicator (AOT40F) did not significantly affect NPP; ii) a differential action of oxidised and reduced nitrogen depositions to NPP was linked to the geographical location; iii) the species-specific variation of NPP caused by combination of pollutants and climatic variables could be a potentially important drive-factor for the plant species' shift as response to the future climate change. - Highlights: ► GLZ Models emphasized the role of combination of variables affecting NPP. ► A differential action of ox-N and red-N deposition to NPP was observed for plants. ► Different responses to climate and pollutants could affect the plant species' shift. - Ozone and nitrogen depositions have non-linear effects on primary productivity of tree species differently distributed in Italy.

Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

Directory of Open Access Journals (Sweden)

Seçil YALAZ

2016-10-01

Full Text Available Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT and to estimate future an equation has created by applying fuzzy least square regression (FLSR method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

Comparison of Classical Linear Regression and Orthogonal Regression According to the Sum of Squares Perpendicular Distances

OpenAIRE

KELEŞ, Taliha; ALTUN, Murat

2016-01-01

Regression analysis is a statistical technique for investigating and modeling the relationship between variables. The purpose of this study was the trivial presentation of the equation for orthogonal regression (OR) and the comparison of classical linear regression (CLR) and OR techniques with respect to the sum of squared perpendicular distances. For that purpose, the analyses were shown by an example. It was found that the sum of squared perpendicular distances of OR is smaller. Thus, it wa...

EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

Science.gov (United States)

Sasaki, Misao; Wands, David

2010-06-01

In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

Inverse estimation of multiple muscle activations based on linear logistic regression.

Science.gov (United States)

Sekiya, Masashi; Tsuji, Toshiaki

2017-07-01

This study deals with a technology to estimate the muscle activity from the movement data using a statistical model. A linear regression (LR) model and artificial neural networks (ANN) have been known as statistical models for such use. Although ANN has a high estimation capability, it is often in the clinical application that the lack of data amount leads to performance deterioration. On the other hand, the LR model has a limitation in generalization performance. We therefore propose a muscle activity estimation method to improve the generalization performance through the use of linear logistic regression model. The proposed method was compared with the LR model and ANN in the verification experiment with 7 participants. As a result, the proposed method showed better generalization performance than the conventional methods in various tasks.

How Robust Is Linear Regression with Dummy Variables?

Science.gov (United States)

Blankmeyer, Eric

2006-01-01

Researchers in education and the social sciences make extensive use of linear regression models in which the dependent variable is continuous-valued while the explanatory variables are a combination of continuous-valued regressors and dummy variables. The dummies partition the sample into groups, some of which may contain only a few observations.…

Neutrosophic Correlation and Simple Linear Regression

Directory of Open Access Journals (Sweden)

A. A. Salama

2014-09-01

Full Text Available Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache. Recently, Salama et al., introduced the concept of correlation coefficient of neutrosophic data. In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces and study some of their properties. Also, we introduce and study the neutrosophic simple linear regression model. Possible applications to data processing are touched upon.

Non-linear DSGE Models and The Central Difference Kalman Filter

DEFF Research Database (Denmark)

Andreasen, Martin Møller

This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Cen- tral Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models...

Investigation of linear regression of EPR dosimetric signal of the man tooth enamel

International Nuclear Information System (INIS)

Pivovarov, S.P.; Rukhin, A.B.; Zhakparov, R.K.; Vasilevskaya, L.A.

2001-01-01

The experimental relations of the EPR radiation signal in samples of man tooth enamel of three donors of different age up to doses 1350 Gy are examined. To all of them the linear regression is applicable. The considerable errors leading to apparent non-linearity are eliminated most. (author)

Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

Science.gov (United States)

Asavaskulkiet, Krissada

2018-04-01

In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.

Distributed Monitoring of the R2 Statistic for Linear Regression

Data.gov (United States)

National Aeronautics and Space Administration — The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and...

Linear regression in astronomy. I

Science.gov (United States)

Isobe, Takashi; Feigelson, Eric D.; Akritas, Michael G.; Babu, Gutti Jogesh

1990-01-01

Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and 'reduced major-axis' regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulas for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulas was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. It is found that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.

Reduction of interferences in graphite furnace atomic absorption spectrometry by multiple linear regression modelling

Science.gov (United States)

Grotti, Marco; Abelmoschi, Maria Luisa; Soggia, Francesco; Tiberiade, Christian; Frache, Roberto

2000-12-01

The multivariate effects of Na, K, Mg and Ca as nitrates on the electrothermal atomisation of manganese, cadmium and iron were studied by multiple linear regression modelling. Since the models proved to efficiently predict the effects of the considered matrix elements in a wide range of concentrations, they were applied to correct the interferences occurring in the determination of trace elements in seawater after pre-concentration of the analytes. In order to obtain a statistically significant number of samples, a large volume of the certified seawater reference materials CASS-3 and NASS-3 was treated with Chelex-100 resin; then, the chelating resin was separated from the solution, divided into several sub-samples, each of them was eluted with nitric acid and analysed by electrothermal atomic absorption spectrometry (for trace element determinations) and inductively coupled plasma optical emission spectrometry (for matrix element determinations). To minimise any other systematic error besides that due to matrix effects, accuracy of the pre-concentration step and contamination levels of the procedure were checked by inductively coupled plasma mass spectrometric measurements. Analytical results obtained by applying the multiple linear regression models were compared with those obtained with other calibration methods, such as external calibration using acid-based standards, external calibration using matrix-matched standards and the analyte addition technique. Empirical models proved to efficiently reduce interferences occurring in the analysis of real samples, allowing an improvement of accuracy better than for other calibration methods.

Detection of epistatic effects with logic regression and a classical linear regression model.

Science.gov (United States)

Malina, Magdalena; Ickstadt, Katja; Schwender, Holger; Posch, Martin; Bogdan, Małgorzata

2014-02-01

To locate multiple interacting quantitative trait loci (QTL) influencing a trait of interest within experimental populations, usually methods as the Cockerham's model are applied. Within this framework, interactions are understood as the part of the joined effect of several genes which cannot be explained as the sum of their additive effects. However, if a change in the phenotype (as disease) is caused by Boolean combinations of genotypes of several QTLs, this Cockerham's approach is often not capable to identify them properly. To detect such interactions more efficiently, we propose a logic regression framework. Even though with the logic regression approach a larger number of models has to be considered (requiring more stringent multiple testing correction) the efficient representation of higher order logic interactions in logic regression models leads to a significant increase of power to detect such interactions as compared to a Cockerham's approach. The increase in power is demonstrated analytically for a simple two-way interaction model and illustrated in more complex settings with simulation study and real data analysis.

Non Linear signa models probing the string structure

International Nuclear Information System (INIS)

Abdalla, E.

1987-01-01

The introduction of a term depending on the extrinsic curvature to the string action, and related non linear sigma models defined on a symmetric space SO(D)/SO(2) x SO(d-2) is descussed . Coupling to fermions are also treated. (author) [pt

Heterotic non-linear sigma models with anti-de Sitter target spaces

International Nuclear Information System (INIS)

Michalogiorgakis, Georgios; Gubser, Steven S.

2006-01-01

We calculate the beta function of non-linear sigma models with S D+1 and AdS D+1 target spaces in a 1/D expansion up to order 1/D 2 and to all orders in α ' . This beta function encodes partial information about the spacetime effective action for the heterotic string to all orders in α ' . We argue that a zero of the beta function, corresponding to a worldsheet CFT with AdS D+1 target space, arises from competition between the one-loop and higher-loop terms, similarly to the bosonic and supersymmetric cases studied previously in [J.J. Friess, S.S. Gubser, Non-linear sigma models with anti-de Sitter target spaces, Nucl. Phys. B 750 (2006) 111-141]. Various critical exponents of the non-linear sigma model are calculated, and checks of the calculation are presented

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

Science.gov (United States)

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

On macroeconomic values investigation using fuzzy linear regression analysis

Directory of Open Access Journals (Sweden)

Richard Pospíšil

2017-06-01

Full Text Available The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets - fuzzy numbers and there is described a fuzzy linear regression model as a fuzzy function with fuzzy numbers as vague parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used. The linear approximation of the vague function together with its possibility area is analytically and graphically expressed. A suitable application is performed in the tasks of the time series fuzzy regression analysis. The time-trend and seasonal cycles including their possibility areas are calculated and expressed. The examples are presented from the economy field, namely the time-development of unemployment, agricultural production and construction respectively between 2009 and 2011 in the Czech Republic. The results are shown in the form of the fuzzy regression models of variables of time series. For the period 2009-2011, the analysis assumptions about seasonal behaviour of variables and the relationship between them were confirmed; in 2010, the system behaved fuzzier and the relationships between the variables were vaguer, that has a lot of causes, from the different elasticity of demand, through state interventions to globalization and transnational impacts.

Linearity and Non-linearity of Photorefractive effect in Materials ...

African Journals Online (AJOL)

In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...

Analysis of γ spectra in airborne radioactivity measurements using multiple linear regressions

International Nuclear Information System (INIS)

Bao Min; Shi Quanlin; Zhang Jiamei

2004-01-01

This paper describes the net peak counts calculating of nuclide 137 Cs at 662 keV of γ spectra in airborne radioactivity measurements using multiple linear regressions. Mathematic model is founded by analyzing every factor that has contribution to Cs peak counts in spectra, and multiple linear regression function is established. Calculating process adopts stepwise regression, and the indistinctive factors are eliminated by F check. The regression results and its uncertainty are calculated using Least Square Estimation, then the Cs peak net counts and its uncertainty can be gotten. The analysis results for experimental spectrum are displayed. The influence of energy shift and energy resolution on the analyzing result is discussed. In comparison with the stripping spectra method, multiple linear regression method needn't stripping radios, and the calculating result has relation with the counts in Cs peak only, and the calculating uncertainty is reduced. (authors)

Linear versus non-linear supersymmetry, in general

Energy Technology Data Exchange (ETDEWEB)

Ferrara, Sergio [Theoretical Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati,Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics and Astronomy, UniversityC.L.A.,Los Angeles, CA 90095-1547 (United States); Kallosh, Renata [SITP and Department of Physics, Stanford University,Stanford, California 94305 (United States); Proeyen, Antoine Van [Institute for Theoretical Physics, Katholieke Universiteit Leuven,Celestijnenlaan 200D, B-3001 Leuven (Belgium); Wrase, Timm [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria)

2016-04-12

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.

Linear versus non-linear supersymmetry, in general

International Nuclear Information System (INIS)

Ferrara, Sergio; Kallosh, Renata; Proeyen, Antoine Van; Wrase, Timm

2016-01-01

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.

Modeling of non-linear CHP efficiency curves in distributed energy systems

DEFF Research Database (Denmark)

Milan, Christian; Stadler, Michael; Cardoso, Gonçalo

2015-01-01

Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...

The number of subjects per variable required in linear regression analyses

NARCIS (Netherlands)

P.C. Austin (Peter); E.W. Steyerberg (Ewout)

2015-01-01

textabstractObjectives To determine the number of independent variables that can be included in a linear regression model. Study Design and Setting We used a series of Monte Carlo simulations to examine the impact of the number of subjects per variable (SPV) on the accuracy of estimated regression

Neutron stars in non-linear coupling models

International Nuclear Information System (INIS)

Taurines, Andre R.; Vasconcellos, Cesar A.Z.; Malheiro, Manuel; Chiapparini, Marcelo

2001-01-01

We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, ∼ 0.72M s un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)

Neutron stars in non-linear coupling models

Energy Technology Data Exchange (ETDEWEB)

Taurines, Andre R.; Vasconcellos, Cesar A.Z. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil); Malheiro, Manuel [Universidade Federal Fluminense, Niteroi, RJ (Brazil); Chiapparini, Marcelo [Universidade do Estado, Rio de Janeiro, RJ (Brazil)

2001-07-01

We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, {approx} 0.72M{sub s}un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)

Linear regression models for quantitative assessment of left ...

African Journals Online (AJOL)

Changes in left ventricular structures and function have been reported in cardiomyopathies. No prediction models have been established in this environment. This study established regression models for prediction of left ventricular structures in normal subjects. A sample of normal subjects was drawn from a large urban ...

Non-renormalizability of supersymmetric non-linear sigma models in four dimensions

International Nuclear Information System (INIS)

Spence, B.

1985-01-01

The one-loop, on-shell, ultraviolet-divergent part of the effective action is calculated for the N=1 and 2 supersymmetric non-linear sigma models in four dimensions. These infinities cannot be absorbed into a redefinition of the bare Kaehler potential and the theories are not renormalizable. (orig.)

Forecasting the EMU inflation rate: Linear econometric vs. non-linear computational models using genetic neural fuzzy systems

DEFF Research Database (Denmark)

Kooths, Stefan; Mitze, Timo Friedel; Ringhut, Eric

2004-01-01

This paper compares the predictive power of linear econometric and non-linear computational models for forecasting the inflation rate in the European Monetary Union (EMU). Various models of both types are developed using different monetary and real activity indicators. They are compared according...

Estimation of error components in a multi-error linear regression model, with an application to track fitting

International Nuclear Information System (INIS)

Fruehwirth, R.

1993-01-01

We present an estimation procedure of the error components in a linear regression model with multiple independent stochastic error contributions. After solving the general problem we apply the results to the estimation of the actual trajectory in track fitting with multiple scattering. (orig.)

Current algebra of classical non-linear sigma models

International Nuclear Information System (INIS)

Forger, M.; Laartz, J.; Schaeper, U.

1992-01-01

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)

Modeling of Soil Aggregate Stability using Support Vector Machines and Multiple Linear Regression

Directory of Open Access Journals (Sweden)

Ali Asghar Besalatpour

2016-02-01

by 20-m digital elevation model (DEM. The data set was divided into two subsets of training and testing. The training subset was randomly chosen from 70% of the total set of the data and the remaining samples (30% of the data were used as the testing set. The correlation coefficient (r, mean square error (MSE, and error percentage (ERROR% between the measured and the predicted GMD values were used to evaluate the performance of the models. Results and Discussion: The description statistics showed that there was little variability in the sample distributions of the variables used in this study to develop the GMD prediction models, indicating that their values were all normally distributed. The constructed SVM model had better performance in predicting GMD compared to the traditional multiple linear regression model. The obtained MSE and r values for the developed SVM model for soil aggregate stability prediction were 0.005 and 0.86, respectively. The obtained ERROR% value for soil aggregate stability prediction using the SVM model was 10.7% while it was 15.7% for the regression model. The scatter plot figures also showed that the SVM model was more accurate in GMD estimation than the MLR model, since the predicted GMD values were closer in agreement with the measured values for most of the samples. The worse performance of the MLR model might be due to the larger amount of data that is required for developing a sustainable regression model compared to intelligent systems. Furthermore, only the linear effects of the predictors on the dependent variable can be extracted by linear models while in many cases the effects may not be linear in nature. Meanwhile, the SVM model is suitable for modelling nonlinear relationships and its major advantage is that the method can be developed without knowing the exact form of the analytical function on which the model should be built. All these indicate that the SVM approach would be a better choice for predicting soil aggregate

A non-linear model of information seeking behaviour

Directory of Open Access Journals (Sweden)

Allen E. Foster

2005-01-01

Full Text Available The results of a qualitative, naturalistic, study of information seeking behaviour are reported in this paper. The study applied the methods recommended by Lincoln and Guba for maximising credibility, transferability, dependability, and confirmability in data collection and analysis. Sampling combined purposive and snowball methods, and led to a final sample of 45 inter-disciplinary researchers from the University of Sheffield. In-depth semi-structured interviews were used to elicit detailed examples of information seeking. Coding of interview transcripts took place in multiple iterations over time and used Atlas-ti software to support the process. The results of the study are represented in a non-linear Model of Information Seeking Behaviour. The model describes three core processes (Opening, Orientation, and Consolidation and three levels of contextual interaction (Internal Context, External Context, and Cognitive Approach, each composed of several individual activities and attributes. The interactivity and shifts described by the model show information seeking to be non-linear, dynamic, holistic, and flowing. The paper concludes by describing the whole model of behaviours as analogous to an artist's palette, in which activities remain available throughout information seeking. A summary of key implications of the model and directions for further research are included.

The algebra of non-local charges in non-linear sigma models

International Nuclear Information System (INIS)

Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.

1994-01-01

It is derived the complete Dirac algebra satisfied by non-local charges conserved in non-linear sigma models. Some examples of calculation are given for the O(N) symmetry group. The resulting algebra corresponds to a saturated cubic deformation (with only maximum order terms) of the Kac-Moody algebra. The results are generalized for when a Wess-Zumino term be present. In that case the algebra contains a minor order correction (sub-saturation). (author). 1 ref

Comparison of height-diameter models based on geographically weighted regressions and linear mixed modelling applied to large scale forest inventory data

Energy Technology Data Exchange (ETDEWEB)

Quirós Segovia, M.; Condés Ruiz, S.; Drápela, K.

2016-07-01

Aim of the study: The main objective of this study was to test Geographically Weighted Regression (GWR) for developing height-diameter curves for forests on a large scale and to compare it with Linear Mixed Models (LMM). Area of study: Monospecific stands of Pinus halepensis Mill. located in the region of Murcia (Southeast Spain). Materials and Methods: The dataset consisted of 230 sample plots (2582 trees) from the Third Spanish National Forest Inventory (SNFI) randomly split into training data (152 plots) and validation data (78 plots). Two different methodologies were used for modelling local (Petterson) and generalized height-diameter relationships (Cañadas I): GWR, with different bandwidths, and linear mixed models. Finally, the quality of the estimated models was compared throughout statistical analysis. Main results: In general, both LMM and GWR provide better prediction capability when applied to a generalized height-diameter function than when applied to a local one, with R2 values increasing from around 0.6 to 0.7 in the model validation. Bias and RMSE were also lower for the generalized function. However, error analysis showed that there were no large differences between these two methodologies, evidencing that GWR provides results which are as good as the more frequently used LMM methodology, at least when no additional measurements are available for calibrating. Research highlights: GWR is a type of spatial analysis for exploring spatially heterogeneous processes. GWR can model spatial variation in tree height-diameter relationship and its regression quality is comparable to LMM. The advantage of GWR over LMM is the possibility to determine the spatial location of every parameter without additional measurements. Abbreviations: GWR (Geographically Weighted Regression); LMM (Linear Mixed Model); SNFI (Spanish National Forest Inventory). (Author)

Daily Suspended Sediment Discharge Prediction Using Multiple Linear Regression and Artificial Neural Network

Science.gov (United States)

Uca; Toriman, Ekhwan; Jaafar, Othman; Maru, Rosmini; Arfan, Amal; Saleh Ahmar, Ansari

2018-01-01

Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D; Keesman, K.J.; Zwart, Heiko J.

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D.; Keesman, K.J.; Zwart, H.

2006-01-01

Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state

Predictive modelling of chromium removal using multiple linear and nonlinear regression with special emphasis on operating parameters of bioelectrochemical reactor.

Science.gov (United States)

More, Anand Govind; Gupta, Sunil Kumar

2018-03-24

Bioelectrochemical system (BES) is a novel, self-sustaining metal removal technology functioning on the utilization of chemical energy of organic matter with the help of microorganisms. Experimental trials of two chambered BES reactor were conducted with varying substrate concentration using sodium acetate (500 mg/L to 2000 mg/L COD) and different initial chromium concentration (Cr i ) (10-100 mg/L) at different cathode pH (pH 1-7). In the current study mathematical models based on multiple linear regression (MLR) and non-linear regression (NLR) approach were developed using laboratory experimental data for determining chromium removal efficiency (CRE) in the cathode chamber of BES. Substrate concentration, rate of substrate consumption, Cr i , pH, temperature and hydraulic retention time (HRT) were the operating process parameters of the reactor considered for development of the proposed models. MLR showed a better correlation coefficient (0.972) as compared to NLR (0.952). Validation of the models using t-test analysis revealed unbiasedness of both the models, with t critical value (2.04) greater than t-calculated values for MLR (-0.708) and NLR (-0.86). The root-mean-square error (RMSE) for MLR and NLR were 5.06 % and 7.45 %, respectively. Comparison between both models suggested MLR to be best suited model for predicting the chromium removal behavior using the BES technology to specify a set of operating conditions for BES. Modelling the behavior of CRE will be helpful for scale up of BES technology at industrial level. Copyright © 2018 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

The non-linear link between electricity consumption and temperature in Europe: A threshold panel approach

Energy Technology Data Exchange (ETDEWEB)

Bessec, Marie [CGEMP, Universite Paris-Dauphine, Place du Marechal de Lattre de Tassigny Paris (France); Fouquau, Julien [LEO, Universite d' Orleans, Faculte de Droit, d' Economie et de Gestion, Rue de Blois, BP 6739, 45067 Orleans Cedex 2 (France)

2008-09-15

This paper investigates the relationship between electricity demand and temperature in the European Union. We address this issue by means of a panel threshold regression model on 15 European countries over the last two decades. Our results confirm the non-linearity of the link between electricity consumption and temperature found in more limited geographical areas in previous studies. By distinguishing between North and South countries, we also find that this non-linear pattern is more pronounced in the warm countries. Finally, rolling regressions show that the sensitivity of electricity consumption to temperature in summer has increased in the recent period. (author)

A Detailed Analytical Study of Non-Linear Semiconductor Device Modelling

Directory of Open Access Journals (Sweden)

Umesh Kumar

1995-01-01

junction diode have been developed. The results of computer simulated examples have been presented in each case. The non-linear lumped model for Gunn is a unified model as it describes the diffusion effects as the-domain traves from cathode to anode. An additional feature of this model is that it describes the domain extinction and nucleation phenomena in Gunn dioder with the help of a simple timing circuit. The non-linear lumped model for SCR is general and is valid under any mode of operation in any circuit environment. The memristive circuit model for p-n junction diodes is capable of simulating realistically the diode’s dynamic behavior under reverse, forward and sinusiodal operating modes. The model uses memristor, the charge-controlled resistor to mimic various second-order effects due to conductivity modulation. It is found that both storage time and fall time of the diode can be accurately predicted.

A novel simple QSAR model for the prediction of anti-HIV activity using multiple linear regression analysis.

Science.gov (United States)

Afantitis, Antreas; Melagraki, Georgia; Sarimveis, Haralambos; Koutentis, Panayiotis A; Markopoulos, John; Igglessi-Markopoulou, Olga

2006-08-01

A quantitative-structure activity relationship was obtained by applying Multiple Linear Regression Analysis to a series of 80 1-[2-hydroxyethoxy-methyl]-6-(phenylthio) thymine (HEPT) derivatives with significant anti-HIV activity. For the selection of the best among 37 different descriptors, the Elimination Selection Stepwise Regression Method (ES-SWR) was utilized. The resulting QSAR model (R (2) (CV) = 0.8160; S (PRESS) = 0.5680) proved to be very accurate both in training and predictive stages.

Linear and non-linear simulation of joints contact surface using ...

African Journals Online (AJOL)

The joint modelling including non-linear effects needs accurate and precise study of their behaviors. When joints are under the dynamic loading, micro, macro- slip happens in contact surface which is non-linear reason of the joint contact surface. The non-linear effects of joint contact surface on total behavior of structure are ...

Non-linear sigma model on the fuzzy supersphere

International Nuclear Information System (INIS)

Kurkcuoglu, Seckin

2004-01-01

In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)

Biostatistics Series Module 6: Correlation and Linear Regression.

Science.gov (United States)

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P correlation coefficient can also be calculated for an idea of the correlation in the population. The value r 2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.

Linear and non-linear quantitative structure-activity relationship models on indole substitution patterns as inhibitors of HIV-1 attachment.

Science.gov (United States)

Nirouei, Mahyar; Ghasemi, Ghasem; Abdolmaleki, Parviz; Tavakoli, Abdolreza; Shariati, Shahab

2012-06-01

The antiviral drugs that inhibit human immunodeficiency virus (HIV) entry to the target cells are already in different phases of clinical trials. They prevent viral entry and have a highly specific mechanism of action with a low toxicity profile. Few QSAR studies have been performed on this group of inhibitors. This study was performed to develop a quantitative structure-activity relationship (QSAR) model of the biological activity of indole glyoxamide derivatives as inhibitors of the interaction between HIV glycoprotein gp120 and host cell CD4 receptors. Forty different indole glyoxamide derivatives were selected as a sample set and geometrically optimized using Gaussian 98W. Different combinations of multiple linear regression (MLR), genetic algorithms (GA) and artificial neural networks (ANN) were then utilized to construct the QSAR models. These models were also utilized to select the most efficient subsets of descriptors in a cross-validation procedure for non-linear log (1/EC50) prediction. The results that were obtained using GA-ANN were compared with MLR-MLR and MLR-ANN models. A high predictive ability was observed for the MLR, MLR-ANN and GA-ANN models, with root mean sum square errors (RMSE) of 0.99, 0.91 and 0.67, respectively (N = 40). In summary, machine learning methods were highly effective in designing QSAR models when compared to statistical method.

On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model

International Nuclear Information System (INIS)

Zamolodchikov, Al.B.

1978-01-01

The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws

Identification of an Equivalent Linear Model for a Non-Linear Time-Variant RC-Structure

DEFF Research Database (Denmark)

Kirkegaard, Poul Henning; Andersen, P.; Brincker, Rune

are investigated and compared with ARMAX models used on a running window. The techniques are evaluated using simulated data generated by the non-linear finite element program SARCOF modeling a 10-storey 3-bay concrete structure subjected to amplitude modulated Gaussian white noise filtered through a Kanai......This paper considers estimation of the maximum softening for a RC-structure subjected to earthquake excitation. The so-called Maximum Softening damage indicator relates the global damage state of the RC-structure to the relative decrease of the fundamental eigenfrequency in an equivalent linear...

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

Science.gov (United States)

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

Non-linear hybrid control oriented modelling of a digital displacement machine

DEFF Research Database (Denmark)

Pedersen, Niels Henrik; Johansen, Per; Andersen, Torben O.

2017-01-01

Proper feedback control of digital fluid power machines (Pressure, flow, torque or speed control) requires a control oriented model, from where the system dynamics can be analyzed, stability can be proven and design criteria can be specified. The development of control oriented models for hydraulic...... Digital Displacement Machines (DDM) is complicated due to non-smooth machine behavior, where the dynamics comprises both analog, digital and non-linear elements. For a full stroke operated DDM the power throughput is altered in discrete levels based on the ratio of activated pressure chambers....... In this paper, a control oriented hybrid model is established, which combines the continuous non-linear pressure chamber dynamics and the discrete shaft position dependent activation of the pressure chambers. The hybrid machine model is further extended to describe the dynamics of a Digital Fluid Power...

Thermal Efficiency Degradation Diagnosis Method Using Regression Model

International Nuclear Information System (INIS)

Jee, Chang Hyun; Heo, Gyun Young; Jang, Seok Won; Lee, In Cheol

2011-01-01

This paper proposes an idea for thermal efficiency degradation diagnosis in turbine cycles, which is based on turbine cycle simulation under abnormal conditions and a linear regression model. The correlation between the inputs for representing degradation conditions (normally unmeasured but intrinsic states) and the simulation outputs (normally measured but superficial states) was analyzed with the linear regression model. The regression models can inversely response an associated intrinsic state for a superficial state observed from a power plant. The diagnosis method proposed herein is classified into three processes, 1) simulations for degradation conditions to get measured states (referred as what-if method), 2) development of the linear model correlating intrinsic and superficial states, and 3) determination of an intrinsic state using the superficial states of current plant and the linear regression model (referred as inverse what-if method). The what-if method is to generate the outputs for the inputs including various root causes and/or boundary conditions whereas the inverse what-if method is the process of calculating the inverse matrix with the given superficial states, that is, component degradation modes. The method suggested in this paper was validated using the turbine cycle model for an operating power plant

A SOCIOLOGICAL ANALYSIS OF THE CHILDBEARING COEFFICIENT IN THE ALTAI REGION BASED ON METHOD OF FUZZY LINEAR REGRESSION

Directory of Open Access Journals (Sweden)

Sergei Vladimirovich Varaksin

2017-06-01

Full Text Available Purpose. Construction of a mathematical model of the dynamics of childbearing change in the Altai region in 2000–2016, analysis of the dynamics of changes in birth rates for multiple age categories of women of childbearing age. Methodology. A auxiliary analysis element is the construction of linear mathematical models of the dynamics of childbearing by using fuzzy linear regression method based on fuzzy numbers. Fuzzy linear regression is considered as an alternative to standard statistical linear regression for short time series and unknown distribution law. The parameters of fuzzy linear and standard statistical regressions for childbearing time series were defined with using the built in language MatLab algorithm. Method of fuzzy linear regression is not used in sociological researches yet. Results. There are made the conclusions about the socio-demographic changes in society, the high efficiency of the demographic policy of the leadership of the region and the country, and the applicability of the method of fuzzy linear regression for sociological analysis.

Predicting musically induced emotions from physiological inputs: linear and neural network models.

Science.gov (United States)

Russo, Frank A; Vempala, Naresh N; Sandstrom, Gillian M

2013-01-01

Listening to music often leads to physiological responses. Do these physiological responses contain sufficient information to infer emotion induced in the listener? The current study explores this question by attempting to predict judgments of "felt" emotion from physiological responses alone using linear and neural network models. We measured five channels of peripheral physiology from 20 participants-heart rate (HR), respiration, galvanic skin response, and activity in corrugator supercilii and zygomaticus major facial muscles. Using valence and arousal (VA) dimensions, participants rated their felt emotion after listening to each of 12 classical music excerpts. After extracting features from the five channels, we examined their correlation with VA ratings, and then performed multiple linear regression to see if a linear relationship between the physiological responses could account for the ratings. Although linear models predicted a significant amount of variance in arousal ratings, they were unable to do so with valence ratings. We then used a neural network to provide a non-linear account of the ratings. The network was trained on the mean ratings of eight of the 12 excerpts and tested on the remainder. Performance of the neural network confirms that physiological responses alone can be used to predict musically induced emotion. The non-linear model derived from the neural network was more accurate than linear models derived from multiple linear regression, particularly along the valence dimension. A secondary analysis allowed us to quantify the relative contributions of inputs to the non-linear model. The study represents a novel approach to understanding the complex relationship between physiological responses and musically induced emotion.

Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

Science.gov (United States)

Bhaduri, Kanishka; Das, Kamalika; Giannella, Chris R.

2011-01-01

The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

Science.gov (United States)

Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert

2011-08-25

Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Directory of Open Access Journals (Sweden)

Sorribas Albert

2011-08-01

Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Application of Hierarchical Linear Models/Linear Mixed-Effects Models in School Effectiveness Research

Science.gov (United States)

Ker, H. W.

2014-01-01

Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…

High-throughput quantitative biochemical characterization of algal biomass by NIR spectroscopy; multiple linear regression and multivariate linear regression analysis.

Science.gov (United States)

Laurens, L M L; Wolfrum, E J

2013-12-18

One of the challenges associated with microalgal biomass characterization and the comparison of microalgal strains and conversion processes is the rapid determination of the composition of algae. We have developed and applied a high-throughput screening technology based on near-infrared (NIR) spectroscopy for the rapid and accurate determination of algal biomass composition. We show that NIR spectroscopy can accurately predict the full composition using multivariate linear regression analysis of varying lipid, protein, and carbohydrate content of algal biomass samples from three strains. We also demonstrate a high quality of predictions of an independent validation set. A high-throughput 96-well configuration for spectroscopy gives equally good prediction relative to a ring-cup configuration, and thus, spectra can be obtained from as little as 10-20 mg of material. We found that lipids exhibit a dominant, distinct, and unique fingerprint in the NIR spectrum that allows for the use of single and multiple linear regression of respective wavelengths for the prediction of the biomass lipid content. This is not the case for carbohydrate and protein content, and thus, the use of multivariate statistical modeling approaches remains necessary.

Alternative regression models to assess increase in childhood BMI

OpenAIRE

Beyerlein, Andreas; Fahrmeir, Ludwig; Mansmann, Ulrich; Toschke, André M

2008-01-01

Abstract Background Body mass index (BMI) data usually have skewed distributions, for which common statistical modeling approaches such as simple linear or logistic regression have limitations. Methods Different regression approaches to predict childhood BMI by goodness-of-fit measures and means of interpretation were compared including generalized linear models (GLMs), quantile regression and Generalized Additive Models for Location, Scale and Shape (GAMLSS). We analyzed data of 4967 childre...

Modeling daily soil temperature over diverse climate conditions in Iran—a comparison of multiple linear regression and support vector regression techniques

Science.gov (United States)

Delbari, Masoomeh; Sharifazari, Salman; Mohammadi, Ehsan

2018-02-01

The knowledge of soil temperature at different depths is important for agricultural industry and for understanding climate change. The aim of this study is to evaluate the performance of a support vector regression (SVR)-based model in estimating daily soil temperature at 10, 30 and 100 cm depth at different climate conditions over Iran. The obtained results were compared to those obtained from a more classical multiple linear regression (MLR) model. The correlation sensitivity for the input combinations and periodicity effect were also investigated. Climatic data used as inputs to the models were minimum and maximum air temperature, solar radiation, relative humidity, dew point, and the atmospheric pressure (reduced to see level), collected from five synoptic stations Kerman, Ahvaz, Tabriz, Saghez, and Rasht located respectively in the hyper-arid, arid, semi-arid, Mediterranean, and hyper-humid climate conditions. According to the results, the performance of both MLR and SVR models was quite well at surface layer, i.e., 10-cm depth. However, SVR performed better than MLR in estimating soil temperature at deeper layers especially 100 cm depth. Moreover, both models performed better in humid climate condition than arid and hyper-arid areas. Further, adding a periodicity component into the modeling process considerably improved the models' performance especially in the case of SVR.

The Lie-Poisson structure of integrable classical non-linear sigma models

International Nuclear Information System (INIS)

Bordemann, M.; Forger, M.; Schaeper, U.; Laartz, J.

1993-01-01

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the r-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrix c. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed. (orig.)

Linear and non-linear energy barriers in systems of interacting single-domain ferromagnetic particles

International Nuclear Information System (INIS)

Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru

2011-01-01

A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.

Determination of regression laws: Linear and nonlinear

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

A detailed mathematical determination of regression laws is presented in the article. Particular emphasis is place on determining the laws of X j on X l to account for source nuclei decay and detector errors in nuclear physics instrumentation. Both linear and nonlinear relations are presented. Linearization of 19 functions is tabulated, including graph, relation, variable substitution, obtained linear function, and remarks. 6 refs., 1 tab

Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules

DEFF Research Database (Denmark)

Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.

2008-01-01

This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiati...... that a description of the non-linear heat transfer is essential. The resulting model is a non-linear first order stochastic differential equation for the heat transfer of the PV component....... heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated facades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered...

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

International Nuclear Information System (INIS)

Fujii, Akira; Kluemper, Andreas

1999-01-01

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

Explorative methods in linear models

DEFF Research Database (Denmark)

Høskuldsson, Agnar

2004-01-01

The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....

STREAMFLOW AND WATER QUALITY REGRESSION MODELING ...

African Journals Online (AJOL)

... downstream Obigbo station show: consistent time-trends in degree of contamination; linear and non-linear relationships for water quality models against total dissolved solids (TDS), total suspended sediment (TSS), chloride, pH and sulphate; and non-linear relationship for streamflow and water quality transport models.

Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

KAUST Repository

Alkhalifah, Tariq Ali

2012-09-25

Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

KAUST Repository

Alkhalifah, Tariq Ali; Choi, Yun Seok

2012-01-01

Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Wavelet regression model in forecasting crude oil price

Science.gov (United States)

Hamid, Mohd Helmie; Shabri, Ani

2017-05-01

This study presents the performance of wavelet multiple linear regression (WMLR) technique in daily crude oil forecasting. WMLR model was developed by integrating the discrete wavelet transform (DWT) and multiple linear regression (MLR) model. The original time series was decomposed to sub-time series with different scales by wavelet theory. Correlation analysis was conducted to assist in the selection of optimal decomposed components as inputs for the WMLR model. The daily WTI crude oil price series has been used in this study to test the prediction capability of the proposed model. The forecasting performance of WMLR model were also compared with regular multiple linear regression (MLR), Autoregressive Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) using root mean square errors (RMSE) and mean absolute errors (MAE). Based on the experimental results, it appears that the WMLR model performs better than the other forecasting technique tested in this study.

Modeling patterns in data using linear and related models

International Nuclear Information System (INIS)

Engelhardt, M.E.

1996-06-01

This report considers the use of linear models for analyzing data related to reliability and safety issues of the type usually associated with nuclear power plants. The report discusses some of the general results of linear regression analysis, such as the model assumptions and properties of the estimators of the parameters. The results are motivated with examples of operational data. Results about the important case of a linear regression model with one covariate are covered in detail. This case includes analysis of time trends. The analysis is applied with two different sets of time trend data. Diagnostic procedures and tests for the adequacy of the model are discussed. Some related methods such as weighted regression and nonlinear models are also considered. A discussion of the general linear model is also included. Appendix A gives some basic SAS programs and outputs for some of the analyses discussed in the body of the report. Appendix B is a review of some of the matrix theoretic results which are useful in the development of linear models

Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.

Science.gov (United States)

Ying, Gui-Shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-04-01

To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly. When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI -0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models. In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.

NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS

Directory of Open Access Journals (Sweden)

Hasan YILDIZ

2004-03-01

Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.

The SR Approach: a new Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

DEFF Research Database (Denmark)

Andreasen, Martin Møller; Christensen, Bent Jesper

This paper suggests a new and easy approach to estimate linear and non-linear dynamic term structure models with latent factors. We impose no distributional assumptions on the factors and they may therefore be non-Gaussian. The novelty of our approach is to use many observables (yields or bonds p...

Generating linear regression model to predict motor functions by use of laser range finder during TUG.

Science.gov (United States)

Adachi, Daiki; Nishiguchi, Shu; Fukutani, Naoto; Hotta, Takayuki; Tashiro, Yuto; Morino, Saori; Shirooka, Hidehiko; Nozaki, Yuma; Hirata, Hinako; Yamaguchi, Moe; Yorozu, Ayanori; Takahashi, Masaki; Aoyama, Tomoki

2017-05-01

The purpose of this study was to investigate which spatial and temporal parameters of the Timed Up and Go (TUG) test are associated with motor function in elderly individuals. This study included 99 community-dwelling women aged 72.9 ± 6.3 years. Step length, step width, single support time, variability of the aforementioned parameters, gait velocity, cadence, reaction time from starting signal to first step, and minimum distance between the foot and a marker placed to 3 in front of the chair were measured using our analysis system. The 10-m walk test, five times sit-to-stand (FTSTS) test, and one-leg standing (OLS) test were used to assess motor function. Stepwise multivariate linear regression analysis was used to determine which TUG test parameters were associated with each motor function test. Finally, we calculated a predictive model for each motor function test using each regression coefficient. In stepwise linear regression analysis, step length and cadence were significantly associated with the 10-m walk test, FTSTS and OLS test. Reaction time was associated with the FTSTS test, and step width was associated with the OLS test. Each predictive model showed a strong correlation with the 10-m walk test and OLS test (P motor function test. Moreover, the TUG test time regarded as the lower extremity function and mobility has strong predictive ability in each motor function test. Copyright © 2017 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

An Ionospheric Index Model based on Linear Regression and Neural Network Approaches

Science.gov (United States)

Tshisaphungo, Mpho; McKinnell, Lee-Anne; Bosco Habarulema, John

2017-04-01

The ionosphere is well known to reflect radio wave signals in the high frequency (HF) band due to the present of electron and ions within the region. To optimise the use of long distance HF communications, it is important to understand the drivers of ionospheric storms and accurately predict the propagation conditions especially during disturbed days. This paper presents the development of an ionospheric storm-time index over the South African region for the application of HF communication users. The model will result into a valuable tool to measure the complex ionospheric behaviour in an operational space weather monitoring and forecasting environment. The development of an ionospheric storm-time index is based on a single ionosonde station data over Grahamstown (33.3°S,26.5°E), South Africa. Critical frequency of the F2 layer (foF2) measurements for a period 1996-2014 were considered for this study. The model was developed based on linear regression and neural network approaches. In this talk validation results for low, medium and high solar activity periods will be discussed to demonstrate model's performance.

NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS

International Nuclear Information System (INIS)

TOMAS, R.; FISCHER, W.; JAIN, A.; LUO, Y.; PILAT, F.

2004-01-01

For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability

Regression modeling of ground-water flow

Science.gov (United States)

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

Science.gov (United States)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Macroscopic and non-linear quantum games

International Nuclear Information System (INIS)

Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

2005-01-01

Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

Iterated non-linear model predictive control based on tubes and contractive constraints.

Science.gov (United States)

Murillo, M; Sánchez, G; Giovanini, L

2016-05-01

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Self-organising mixture autoregressive model for non-stationary time series modelling.

Science.gov (United States)

Ni, He; Yin, Hujun

2008-12-01

Modelling non-stationary time series has been a difficult task for both parametric and nonparametric methods. One promising solution is to combine the flexibility of nonparametric models with the simplicity of parametric models. In this paper, the self-organising mixture autoregressive (SOMAR) network is adopted as a such mixture model. It breaks time series into underlying segments and at the same time fits local linear regressive models to the clusters of segments. In such a way, a global non-stationary time series is represented by a dynamic set of local linear regressive models. Neural gas is used for a more flexible structure of the mixture model. Furthermore, a new similarity measure has been introduced in the self-organising network to better quantify the similarity of time series segments. The network can be used naturally in modelling and forecasting non-stationary time series. Experiments on artificial, benchmark time series (e.g. Mackey-Glass) and real-world data (e.g. numbers of sunspots and Forex rates) are presented and the results show that the proposed SOMAR network is effective and superior to other similar approaches.

Parametric and Non-Parametric System Modelling

DEFF Research Database (Denmark)

Nielsen, Henrik Aalborg

1999-01-01

the focus is on combinations of parametric and non-parametric methods of regression. This combination can be in terms of additive models where e.g. one or more non-parametric term is added to a linear regression model. It can also be in terms of conditional parametric models where the coefficients...... considered. It is shown that adaptive estimation in conditional parametric models can be performed by combining the well known methods of local polynomial regression and recursive least squares with exponential forgetting. The approach used for estimation in conditional parametric models also highlights how...... networks is included. In this paper, neural networks are used for predicting the electricity production of a wind farm. The results are compared with results obtained using an adaptively estimated ARX-model. Finally, two papers on stochastic differential equations are included. In the first paper, among...

Standardizing effect size from linear regression models with log-transformed variables for meta-analysis.

Science.gov (United States)

Rodríguez-Barranco, Miguel; Tobías, Aurelio; Redondo, Daniel; Molina-Portillo, Elena; Sánchez, María José

2017-03-17

Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized. We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed. In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese. The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables.

COLOR IMAGE RETRIEVAL BASED ON FEATURE FUSION THROUGH MULTIPLE LINEAR REGRESSION ANALYSIS

Directory of Open Access Journals (Sweden)

K. Seetharaman

2015-08-01

Full Text Available This paper proposes a novel technique based on feature fusion using multiple linear regression analysis, and the least-square estimation method is employed to estimate the parameters. The given input query image is segmented into various regions according to the structure of the image. The color and texture features are extracted on each region of the query image, and the features are fused together using the multiple linear regression model. The estimated parameters of the model, which is modeled based on the features, are formed as a vector called a feature vector. The Canberra distance measure is adopted to compare the feature vectors of the query and target images. The F-measure is applied to evaluate the performance of the proposed technique. The obtained results expose that the proposed technique is comparable to the other existing techniques.

Non-linear time variant model intended for polypyrrole-based actuators

Science.gov (United States)

Farajollahi, Meisam; Madden, John D. W.; Sassani, Farrokh

2014-03-01

Polypyrrole-based actuators are of interest due to their biocompatibility, low operation voltage and relatively high strain and force. Modeling and simulation are very important to predict the behaviour of each actuator. To develop an accurate model, we need to know the electro-chemo-mechanical specifications of the Polypyrrole. In this paper, the non-linear time-variant model of Polypyrrole film is derived and proposed using a combination of an RC transmission line model and a state space representation. The model incorporates the potential dependent ionic conductivity. A function of ionic conductivity of Polypyrrole vs. local charge is proposed and implemented in the non-linear model. Matching of the measured and simulated electrical response suggests that ionic conductivity of Polypyrrole decreases significantly at negative potential vs. silver/silver chloride and leads to reduced current in the cyclic voltammetry (CV) tests. The next stage is to relate the distributed charging of the polymer to actuation via the strain to charge ratio. Further work is also needed to identify ionic and electronic conductivities as well as capacitance as a function of oxidation state so that a fully predictive model can be created.

Estimating leaf photosynthetic pigments information by stepwise multiple linear regression analysis and a leaf optical model

Science.gov (United States)

Liu, Pudong; Shi, Runhe; Wang, Hong; Bai, Kaixu; Gao, Wei

2014-10-01

Leaf pigments are key elements for plant photosynthesis and growth. Traditional manual sampling of these pigments is labor-intensive and costly, which also has the difficulty in capturing their temporal and spatial characteristics. The aim of this work is to estimate photosynthetic pigments at large scale by remote sensing. For this purpose, inverse model were proposed with the aid of stepwise multiple linear regression (SMLR) analysis. Furthermore, a leaf radiative transfer model (i.e. PROSPECT model) was employed to simulate the leaf reflectance where wavelength varies from 400 to 780 nm at 1 nm interval, and then these values were treated as the data from remote sensing observations. Meanwhile, simulated chlorophyll concentration (Cab), carotenoid concentration (Car) and their ratio (Cab/Car) were taken as target to build the regression model respectively. In this study, a total of 4000 samples were simulated via PROSPECT with different Cab, Car and leaf mesophyll structures as 70% of these samples were applied for training while the last 30% for model validation. Reflectance (r) and its mathematic transformations (1/r and log (1/r)) were all employed to build regression model respectively. Results showed fair agreements between pigments and simulated reflectance with all adjusted coefficients of determination (R2) larger than 0.8 as 6 wavebands were selected to build the SMLR model. The largest value of R2 for Cab, Car and Cab/Car are 0.8845, 0.876 and 0.8765, respectively. Meanwhile, mathematic transformations of reflectance showed little influence on regression accuracy. We concluded that it was feasible to estimate the chlorophyll and carotenoids and their ratio based on statistical model with leaf reflectance data.

Generalised linear models for correlated pseudo-observations, with applications to multi-state models

DEFF Research Database (Denmark)

Andersen, Per Kragh; Klein, John P.; Rosthøj, Susanne

2003-01-01

Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model......Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model...

Reflexion on linear regression trip production modelling method for ensuring good model quality

Science.gov (United States)

Suprayitno, Hitapriya; Ratnasari, Vita

2017-11-01

Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.

Time series regression model for infectious disease and weather.

Science.gov (United States)

Imai, Chisato; Armstrong, Ben; Chalabi, Zaid; Mangtani, Punam; Hashizume, Masahiro

2015-10-01

Time series regression has been developed and long used to evaluate the short-term associations of air pollution and weather with mortality or morbidity of non-infectious diseases. The application of the regression approaches from this tradition to infectious diseases, however, is less well explored and raises some new issues. We discuss and present potential solutions for five issues often arising in such analyses: changes in immune population, strong autocorrelations, a wide range of plausible lag structures and association patterns, seasonality adjustments, and large overdispersion. The potential approaches are illustrated with datasets of cholera cases and rainfall from Bangladesh and influenza and temperature in Tokyo. Though this article focuses on the application of the traditional time series regression to infectious diseases and weather factors, we also briefly introduce alternative approaches, including mathematical modeling, wavelet analysis, and autoregressive integrated moving average (ARIMA) models. Modifications proposed to standard time series regression practice include using sums of past cases as proxies for the immune population, and using the logarithm of lagged disease counts to control autocorrelation due to true contagion, both of which are motivated from "susceptible-infectious-recovered" (SIR) models. The complexity of lag structures and association patterns can often be informed by biological mechanisms and explored by using distributed lag non-linear models. For overdispersed models, alternative distribution models such as quasi-Poisson and negative binomial should be considered. Time series regression can be used to investigate dependence of infectious diseases on weather, but may need modifying to allow for features specific to this context. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Separation-induced boundary layer transition: Modeling with a non-linear eddy-viscosity model coupled with the laminar kinetic energy equation

International Nuclear Information System (INIS)

Vlahostergios, Z.; Yakinthos, K.; Goulas, A.

2009-01-01

We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.

The Importance of Non-Linearity on Turbulent Fluxes

DEFF Research Database (Denmark)

Rokni, Masoud

2007-01-01

Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...

A comparison of non-homogeneous Markov regression models with application to Alzheimer’s disease progression

Science.gov (United States)

Hubbard, R. A.; Zhou, X.H.

2011-01-01

Markov regression models are useful tools for estimating the impact of risk factors on rates of transition between multiple disease states. Alzheimer’s disease (AD) is an example of a multi-state disease process in which great interest lies in identifying risk factors for transition. In this context, non-homogeneous models are required because transition rates change as subjects age. In this report we propose a non-homogeneous Markov regression model that allows for reversible and recurrent disease states, transitions among multiple states between observations, and unequally spaced observation times. We conducted simulation studies to demonstrate performance of estimators for covariate effects from this model and compare performance with alternative models when the underlying non-homogeneous process was correctly specified and under model misspecification. In simulation studies, we found that covariate effects were biased if non-homogeneity of the disease process was not accounted for. However, estimates from non-homogeneous models were robust to misspecification of the form of the non-homogeneity. We used our model to estimate risk factors for transition to mild cognitive impairment (MCI) and AD in a longitudinal study of subjects included in the National Alzheimer’s Coordinating Center’s Uniform Data Set. Using our model, we found that subjects with MCI affecting multiple cognitive domains were significantly less likely to revert to normal cognition. PMID:22419833

Predicting Fuel Ignition Quality Using 1H NMR Spectroscopy and Multiple Linear Regression

KAUST Repository

Abdul Jameel, Abdul Gani; Naser, Nimal; Emwas, Abdul-Hamid M.; Dooley, Stephen; Sarathy, Mani

2016-01-01

An improved model for the prediction of ignition quality of hydrocarbon fuels has been developed using 1H nuclear magnetic resonance (NMR) spectroscopy and multiple linear regression (MLR) modeling. Cetane number (CN) and derived cetane number (DCN

Non linear viscoelastic models

DEFF Research Database (Denmark)

Agerkvist, Finn T.

2011-01-01

Viscoelastic eects are often present in loudspeaker suspensions, this can be seen in the displacement transfer function which often shows a frequency dependent value below the resonance frequency. In this paper nonlinear versions of the standard linear solid model (SLS) are investigated....... The simulations show that the nonlinear version of the Maxwell SLS model can result in a time dependent small signal stiness while the Kelvin Voight version does not....

The use of artificial neural networks and multiple linear regression to predict rate of medical waste generation

International Nuclear Information System (INIS)

Jahandideh, Sepideh; Jahandideh, Samad; Asadabadi, Ebrahim Barzegari; Askarian, Mehrdad; Movahedi, Mohammad Mehdi; Hosseini, Somayyeh; Jahandideh, Mina

2009-01-01

Prediction of the amount of hospital waste production will be helpful in the storage, transportation and disposal of hospital waste management. Based on this fact, two predictor models including artificial neural networks (ANNs) and multiple linear regression (MLR) were applied to predict the rate of medical waste generation totally and in different types of sharp, infectious and general. In this study, a 5-fold cross-validation procedure on a database containing total of 50 hospitals of Fars province (Iran) were used to verify the performance of the models. Three performance measures including MAR, RMSE and R 2 were used to evaluate performance of models. The MLR as a conventional model obtained poor prediction performance measure values. However, MLR distinguished hospital capacity and bed occupancy as more significant parameters. On the other hand, ANNs as a more powerful model, which has not been introduced in predicting rate of medical waste generation, showed high performance measure values, especially 0.99 value of R 2 confirming the good fit of the data. Such satisfactory results could be attributed to the non-linear nature of ANNs in problem solving which provides the opportunity for relating independent variables to dependent ones non-linearly. In conclusion, the obtained results showed that our ANN-based model approach is very promising and may play a useful role in developing a better cost-effective strategy for waste management in future.

Non Linear Modelling and Control of Hydraulic Actuators

Directory of Open Access Journals (Sweden)

B. Šulc

2002-01-01

Full Text Available This paper deals with non-linear modelling and control of a differential hydraulic actuator. The nonlinear state space equations are derived from basic physical laws. They are more powerful than the transfer function in the case of linear models, and they allow the application of an object oriented approach in simulation programs. The effects of all friction forces (static, Coulomb and viscous have been modelled, and many phenomena that are usually neglected are taken into account, e.g., the static term of friction, the leakage between the two chambers and external space. Proportional Differential (PD and Fuzzy Logic Controllers (FLC have been applied in order to make a comparison by means of simulation. Simulation is performed using Matlab/Simulink, and some of the results are compared graphically. FLC is tuned in a such way that it produces a constant control signal close to its maximum (or minimum, where possible. In the case of PD control the occurrence of peaks cannot be avoided. These peaks produce a very high velocity that oversteps the allowed values.

Finite Algorithms for Robust Linear Regression

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun

1990-01-01

The Huber M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may...

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Linear Regression Analysis

CERN Document Server

Seber, George A F

2012-01-01

Concise, mathematically clear, and comprehensive treatment of the subject.* Expanded coverage of diagnostics and methods of model fitting.* Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models.* More than 200 problems throughout the book plus outline solutions for the exercises.* This revision has been extensively class-tested.

Focused information criterion and model averaging based on weighted composite quantile regression

KAUST Repository

Xu, Ganggang

2013-08-13

We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non-parametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the frequentist model averaging WCQR-estimator of a focused parameter is a non-linear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. With properly chosen weights, the focused information criterion based WCQR estimators are not only robust to outliers and non-normal residuals but also can achieve efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedure. © 2013 Board of the Foundation of the Scandinavian Journal of Statistics..

Reliability of the Load-Velocity Relationship Obtained Through Linear and Polynomial Regression Models to Predict the One-Repetition Maximum Load.

Science.gov (United States)

Pestaña-Melero, Francisco Luis; Haff, G Gregory; Rojas, Francisco Javier; Pérez-Castilla, Alejandro; García-Ramos, Amador

2017-12-18

This study aimed to compare the between-session reliability of the load-velocity relationship between (1) linear vs. polynomial regression models, (2) concentric-only vs. eccentric-concentric bench press variants, as well as (3) the within-participants vs. the between-participants variability of the velocity attained at each percentage of the one-repetition maximum (%1RM). The load-velocity relationship of 30 men (age: 21.2±3.8 y; height: 1.78±0.07 m, body mass: 72.3±7.3 kg; bench press 1RM: 78.8±13.2 kg) were evaluated by means of linear and polynomial regression models in the concentric-only and eccentric-concentric bench press variants in a Smith Machine. Two sessions were performed with each bench press variant. The main findings were: (1) first-order-polynomials (CV: 4.39%-4.70%) provided the load-velocity relationship with higher reliability than second-order-polynomials (CV: 4.68%-5.04%); (2) the reliability of the load-velocity relationship did not differ between the concentric-only and eccentric-concentric bench press variants; (3) the within-participants variability of the velocity attained at each %1RM was markedly lower than the between-participants variability. Taken together, these results highlight that, regardless of the bench press variant considered, the individual determination of the load-velocity relationship by a linear regression model could be recommended to monitor and prescribe the relative load in the Smith machine bench press exercise.

Trend analysis by a piecewise linear regression model applied to surface air temperatures in Southeastern Spain (1973–2014)

OpenAIRE

Campra, Pablo; Morales, Maria

2016-01-01

The magnitude of the trends of environmental and climatic changes is mostly derived from the slopes of the linear trends using ordinary least-square fitting. An alternative flexible fitting model, piecewise regression, has been applied here to surface air temperature records in southeastern Spain for the recent warming period (1973–2014) to gain accuracy in the description of the inner structure of change, dividing the time series into linear segments with different slopes. Breakpoint y...

Association of footprint measurements with plantar kinetics: a linear regression model.

Science.gov (United States)

Fascione, Jeanna M; Crews, Ryan T; Wrobel, James S

2014-03-01

The use of foot measurements to classify morphology and interpret foot function remains one of the focal concepts of lower-extremity biomechanics. However, only 27% to 55% of midfoot variance in foot pressures has been determined in the most comprehensive models. We investigated whether dynamic walking footprint measurements are associated with inter-individual foot loading variability. Thirty individuals (15 men and 15 women; mean ± SD age, 27.17 ± 2.21 years) walked at a self-selected speed over an electronic pedography platform using the midgait technique. Kinetic variables (contact time, peak pressure, pressure-time integral, and force-time integral) were collected for six masked regions. Footprints were digitized for area and linear boundaries using digital photo planimetry software. Six footprint measurements were determined: contact area, footprint index, arch index, truncated arch index, Chippaux-Smirak index, and Staheli index. Linear regression analysis with a Bonferroni adjustment was performed to determine the association between the footprint measurements and each of the kinetic variables. The findings demonstrate that a relationship exists between increased midfoot contact and increased kinetic values in respective locations. Many of these variables produced large effect sizes while describing 38% to 71% of the common variance of select plantar kinetic variables in the medial midfoot region. In addition, larger footprints were associated with larger kinetic values at the medial heel region and both masked forefoot regions. Dynamic footprint measurements are associated with dynamic plantar loading kinetics, with emphasis on the midfoot region.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

Science.gov (United States)

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Science.gov (United States)

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Fourier imaging of non-linear structure formation

Energy Technology Data Exchange (ETDEWEB)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

2017-04-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Fourier imaging of non-linear structure formation

International Nuclear Information System (INIS)

Brandbyge, Jacob; Hannestad, Steen

2017-01-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

A Non-Gaussian Spatial Generalized Linear Latent Variable Model

KAUST Repository

Irincheeva, Irina; Cantoni, Eva; Genton, Marc G.

2012-01-01

We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.

A Non-Gaussian Spatial Generalized Linear Latent Variable Model

KAUST Repository

Irincheeva, Irina

2012-08-03

We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.

A parametric FE modeling of brake for non-linear analysis

Energy Technology Data Exchange (ETDEWEB)

Ahmed,Ibrahim; Fatouh, Yasser [Automotive and Tractors Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt); Aly, Wael [Refrigeration and Air-Conditioning Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt)

2013-07-01

A parametric modeling of a drum brake based on 3-D Finite Element Methods (FEM) for non-contact analysis is presented. Many parameters are examined during this study such as the effect of drum-lining interface stiffness, coefficient of friction, and line pressure on the interface contact. Firstly, the modal analysis of the drum brake is also studied to get the natural frequency and instability of the drum to facilitate transforming the modal elements to non-contact elements. It is shown that the Unsymmetric solver of the modal analysis is efficient enough to solve this linear problem after transforming the non-linear behavior of the contact between the drum and the lining to a linear behavior. A SOLID45 which is a linear element is used in the modal analysis and then transferred to non-linear elements which are Targe170 and Conta173 that represent the drum and lining for contact analysis study. The contact analysis problems are highly non-linear and require significant computer resources to solve it, however, the contact problem give two significant difficulties. Firstly, the region of contact is not known based on the boundary conditions such as line pressure, and drum and friction material specs. Secondly, these contact problems need to take the friction into consideration. Finally, it showed a good distribution of the nodal reaction forces on the slotted lining contact surface and existing of the slot in the middle of the lining can help in wear removal due to the friction between the lining and the drum. Accurate contact stiffness can give a good representation for the pressure distribution between the lining and the drum. However, a full contact of the front part of the slotted lining could occur in case of 20, 40, 60 and 80 bar of piston pressure and a partially contact between the drum and lining can occur in the rear part of the slotted lining.

Mathematical models of non-linear phenomena, processes and systems: from molecular scale to planetary atmosphere

CERN Document Server

2013-01-01

This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.

Linear velocity fields in non-Gaussian models for large-scale structure

Science.gov (United States)

Scherrer, Robert J.

1992-01-01

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

Regression-based model of skin diffuse reflectance for skin color analysis

Science.gov (United States)

Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi

2008-11-01

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

Least square regression based integrated multi-parameteric demand modeling for short term load forecasting

International Nuclear Information System (INIS)

Halepoto, I.A.; Uqaili, M.A.

2014-01-01

Nowadays, due to power crisis, electricity demand forecasting is deemed an important area for socioeconomic development and proper anticipation of the load forecasting is considered essential step towards efficient power system operation, scheduling and planning. In this paper, we present STLF (Short Term Load Forecasting) using multiple regression techniques (i.e. linear, multiple linear, quadratic and exponential) by considering hour by hour load model based on specific targeted day approach with temperature variant parameter. The proposed work forecasts the future load demand correlation with linear and non-linear parameters (i.e. considering temperature in our case) through different regression approaches. The overall load forecasting error is 2.98% which is very much acceptable. From proposed regression techniques, Quadratic Regression technique performs better compared to than other techniques because it can optimally fit broad range of functions and data sets. The work proposed in this paper, will pave a path to effectively forecast the specific day load with multiple variance factors in a way that optimal accuracy can be maintained. (author)

An axisymmetrical non-linear finite element model for induction heating in injection molding tools

DEFF Research Database (Denmark)

Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano

2016-01-01

To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed......, including the non-linear temperature dependent magnetic data described by a three-parameter modified Frohlich equation fitted to the magnetic saturation curve, and solved with an iterative procedure. The numerical calculations are compared with experiments conducted with two types of induction coils, built...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...

Quantum non-local charges and absence of particle production in the two-dimensional non-linear sigma-model

International Nuclear Information System (INIS)

Luescher, M.

1977-12-01

Conserved non-local charges are shown to exist in the quantum non-linear sigma-model by a non-perturbative method. They imply the absence of particle production and the 'factorization equations' for the two particle S-matrix, which can then be calculated explicitly. (Auth.)

Linear regression analysis: part 14 of a series on evaluation of scientific publications.

Science.gov (United States)

Schneider, Astrid; Hommel, Gerhard; Blettner, Maria

2010-11-01

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.

Power properties of invariant tests for spatial autocorrelation in linear regression

NARCIS (Netherlands)

Martellosio, F.

2006-01-01

Many popular tests for residual spatial autocorrelation in the context of the linear regression model belong to the class of invariant tests. This paper derives a number of exact properties of the power function of such tests. In particular, we extend the work of Krämer (2005, Journal of Statistical

Analysis of interactive fixed effects dynamic linear panel regression with measurement error

OpenAIRE

Nayoung Lee; Hyungsik Roger Moon; Martin Weidner

2011-01-01

This paper studies a simple dynamic panel linear regression model with interactive fixed effects in which the variable of interest is measured with error. To estimate the dynamic coefficient, we consider the least-squares minimum distance (LS-MD) estimation method.

Phenomenology of non-minimal supersymmetric models at linear colliders

International Nuclear Information System (INIS)

Porto, Stefano

2015-06-01

The focus of this thesis is on the phenomenology of several non-minimal supersymmetric models in the context of future linear colliders (LCs). Extensions of the minimal supersymmetric Standard Model (MSSM) may accommodate the observed Higgs boson mass at about 125 GeV in a more natural way than the MSSM, with a richer phenomenology. We consider both F-term extensions of the MSSM, as for instance the non-minimal supersymmetric Standard Model (NMSSM), as well as D-terms extensions arising at low energies from gauge extended supersymmetric models. The NMSSM offers a solution to the μ-problem with an additional gauge singlet supermultiplet. The enlarged neutralino sector of the NMSSM can be accurately studied at a LC and used to distinguish the model from the MSSM. We show that exploiting the power of the polarised beams of a LC can be used to reconstruct the neutralino and chargino sector and eventually distinguish the NMSSM even considering challenging scenarios that resemble the MSSM. Non-decoupling D-terms extensions of the MSSM can raise the tree-level Higgs mass with respect to the MSSM. This is done through additional contributions to the Higgs quartic potential, effectively generated by an extended gauge group. We study how this can happen and we show how these additional non-decoupling D-terms affect the SM-like Higgs boson couplings to fermions and gauge bosons. We estimate how the deviations from the SM couplings can be spotted at the Large Hadron Collider (LHC) and at the International Linear Collider (ILC), showing how the ILC would be suitable for the model identication. Since our results prove that a linear collider is a fundamental machine for studying supersymmetry phenomenology at a high level of precision, we argue that also a thorough comprehension of the physics at the interaction point (IP) of a LC is needed. Therefore, we finally consider the possibility of observing intense electromagnetic field effects and nonlinear quantum electrodynamics

Perfect observables for the hierarchical non-linear O(N)-invariant σ-model

International Nuclear Information System (INIS)

Wieczerkowski, C.; Xylander, Y.

1995-05-01

We compute moving eigenvalues and the eigenvectors of the linear renormalization group transformation for observables along the renormalized trajectory of the hierarchical non-linear O(N)-invariant σ-model by means of perturbation theory in the running coupling constant. Moving eigenvectors are defined as solutions to a Callan-Symanzik type equation. (orig.)

Poisson Mixture Regression Models for Heart Disease Prediction.

Science.gov (United States)

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

Science.gov (United States)

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

A non-Linear transport model for determining shale rock characteristics

Science.gov (United States)

Ali, Iftikhar; Malik, Nadeem

2016-04-01

Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007

Linear regression models and k-means clustering for statistical analysis of fNIRS data.

Science.gov (United States)

Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro

2015-02-01

We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets.

Multiple Linear Regression: A Realistic Reflector.

Science.gov (United States)

Nutt, A. T.; Batsell, R. R.

Examples of the use of Multiple Linear Regression (MLR) techniques are presented. This is done to show how MLR aids data processing and decision-making by providing the decision-maker with freedom in phrasing questions and by accurately reflecting the data on hand. A brief overview of the rationale underlying MLR is given, some basic definitions…

Generalized non-linear Schroedinger hierarchy

International Nuclear Information System (INIS)

Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

1994-01-01

The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy

Duality in non-linear B and F models: equivalence between self-dual and topologically massive Born-Infeld B and F models

International Nuclear Information System (INIS)

Menezes, R.; Nascimento, J.R.S.; Ribeiro, R.F.; Wotzasek, C.

2002-01-01

We study the dual equivalence between the non-linear generalization of the self-dual (NSD BF ) and the topologically massive B and F models with particular emphasis on the non-linear electrodynamics proposed by Born and Infeld. This is done through a dynamical gauge embedding of the non-linear self-dual model yielding to a gauge invariant and dynamically equivalent theory. We clearly show that non-polinomial NSD BF models can be map, through a properly defined duality transformation into TM BF actions. The general result obtained is then particularized for a number of examples, including the Born-Infeld-BF (BIBF) model that has experienced a revival in the recent literature

Noise and non-linearities in high-throughput data

International Nuclear Information System (INIS)

Nguyen, Viet-Anh; Lió, Pietro; Koukolíková-Nicola, Zdena; Bagnoli, Franco

2009-01-01

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets

Estimating severity of sideways fall using a generic multi linear regression model based on kinematic input variables.

Science.gov (United States)

van der Zijden, A M; Groen, B E; Tanck, E; Nienhuis, B; Verdonschot, N; Weerdesteyn, V

2017-03-21

Many research groups have studied fall impact mechanics to understand how fall severity can be reduced to prevent hip fractures. Yet, direct impact force measurements with force plates are restricted to a very limited repertoire of experimental falls. The purpose of this study was to develop a generic model for estimating hip impact forces (i.e. fall severity) in in vivo sideways falls without the use of force plates. Twelve experienced judokas performed sideways Martial Arts (MA) and Block ('natural') falls on a force plate, both with and without a mat on top. Data were analyzed to determine the hip impact force and to derive 11 selected (subject-specific and kinematic) variables. Falls from kneeling height were used to perform a stepwise regression procedure to assess the effects of these input variables and build the model. The final model includes four input variables, involving one subject-specific measure and three kinematic variables: maximum upper body deceleration, body mass, shoulder angle at the instant of 'maximum impact' and maximum hip deceleration. The results showed that estimated and measured hip impact forces were linearly related (explained variances ranging from 46 to 63%). Hip impact forces of MA falls onto the mat from a standing position (3650±916N) estimated by the final model were comparable with measured values (3698±689N), even though these data were not used for training the model. In conclusion, a generic linear regression model was developed that enables the assessment of fall severity through kinematic measures of sideways falls, without using force plates. Copyright © 2017 Elsevier Ltd. All rights reserved.

Non-Linear Rheological Properties and Neutron Scattering Investigation on Dilute Ring-Linear Blends

DEFF Research Database (Denmark)

Pyckhout-Hintzen, W.; Bras, A.R.; Wischnewski, A.

in a filament stretching rheometer, followed by quenching, strong anisotropic scattering patterns were obtained which were described by affinely deformed rings which function as giant, polymeric chemical crosslinks or sliplinks and more or less isotropic topological contributions from the entangling...... with interpenetrating linear chains. At the same time the non-linear rheological and mechanical data fit to a non-affine slip-tube model as for moderately crosslinked networks and to interchain pressure models or a modified non-linear Doi-Edwards description for the observed strain hardening during the extensional...

A note on the relationships between multiple imputation, maximum likelihood and fully Bayesian methods for missing responses in linear regression models.

Science.gov (United States)

Chen, Qingxia; Ibrahim, Joseph G

2014-07-01

Multiple Imputation, Maximum Likelihood and Fully Bayesian methods are the three most commonly used model-based approaches in missing data problems. Although it is easy to show that when the responses are missing at random (MAR), the complete case analysis is unbiased and efficient, the aforementioned methods are still commonly used in practice for this setting. To examine the performance of and relationships between these three methods in this setting, we derive and investigate small sample and asymptotic expressions of the estimates and standard errors, and fully examine how these estimates are related for the three approaches in the linear regression model when the responses are MAR. We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case estimates under general conditions. One simulation and a real data set from a liver cancer clinical trial are given to compare the properties of these methods when the responses are MAR.

Study on non-linear bistable dynamics model based EEG signal discrimination analysis method.

Science.gov (United States)

Ying, Xiaoguo; Lin, Han; Hui, Guohua

2015-01-01

Electroencephalogram (EEG) is the recording of electrical activity along the scalp. EEG measures voltage fluctuations generating from ionic current flows within the neurons of the brain. EEG signal is looked as one of the most important factors that will be focused in the next 20 years. In this paper, EEG signal discrimination based on non-linear bistable dynamical model was proposed. EEG signals were processed by non-linear bistable dynamical model, and features of EEG signals were characterized by coherence index. Experimental results showed that the proposed method could properly extract the features of different EEG signals.

Improvement of Storm Forecasts Using Gridded Bayesian Linear Regression for Northeast United States

Science.gov (United States)

Yang, J.; Astitha, M.; Schwartz, C. S.

2017-12-01

Bayesian linear regression (BLR) is a post-processing technique in which regression coefficients are derived and used to correct raw forecasts based on pairs of observation-model values. This study presents the development and application of a gridded Bayesian linear regression (GBLR) as a new post-processing technique to improve numerical weather prediction (NWP) of rain and wind storm forecasts over northeast United States. Ten controlled variables produced from ten ensemble members of the National Center for Atmospheric Research (NCAR) real-time prediction system are used for a GBLR model. In the GBLR framework, leave-one-storm-out cross-validation is utilized to study the performances of the post-processing technique in a database composed of 92 storms. To estimate the regression coefficients of the GBLR, optimization procedures that minimize the systematic and random error of predicted atmospheric variables (wind speed, precipitation, etc.) are implemented for the modeled-observed pairs of training storms. The regression coefficients calculated for meteorological stations of the National Weather Service are interpolated back to the model domain. An analysis of forecast improvements based on error reductions during the storms will demonstrate the value of GBLR approach. This presentation will also illustrate how the variances are optimized for the training partition in GBLR and discuss the verification strategy for grid points where no observations are available. The new post-processing technique is successful in improving wind speed and precipitation storm forecasts using past event-based data and has the potential to be implemented in real-time.

Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients

Science.gov (United States)

Gorgees, HazimMansoor; Mahdi, FatimahAssim

2018-05-01

This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.

Non Abelian T-duality in Gauged Linear Sigma Models

Science.gov (United States)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Weak ωNN coupling in the non-linear chiral model

International Nuclear Information System (INIS)

Shmatikov, M.

1988-01-01

In the non-linear chiral model with the soliton solution stabilized by the ω-meson field the weak ωNN coupling constants are calculated. Applying the vector dominance model for the isoscalar current the constant of the isoscalar P-odd ωNN interaction h ω (0) =0 is obtained while the constant of the isovector (of the Lagrangian of the ωNN interaction proves to be h ω (1) ≅ 1.0x10 -7

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

Science.gov (United States)

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Material model for non-linear finite element analyses of large concrete structures

NARCIS (Netherlands)

Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.

2016-01-01

A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

International Nuclear Information System (INIS)

Patel, R; McWilliam, S; Popov, A A

2014-01-01

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations. (paper)

Non-linear dynamics in Parkinsonism

Directory of Open Access Journals (Sweden)

Olivier eDarbin

2013-12-01

Full Text Available Over the last 30 years, the functions (and dysfunctions of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis". In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively.More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e. parkinsonism, dyskinesia, healthy control and are responsive to treatments (i.e. L-DOPA,DBS. A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG, muscular activities (EMG or kinetic of motor symptoms (tremor, gait of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity and hypokinesia.

Multi-step polynomial regression method to model and forecast malaria incidence.

Directory of Open Access Journals (Sweden)

Chandrajit Chatterjee

Full Text Available Malaria is one of the most severe problems faced by the world even today. Understanding the causative factors such as age, sex, social factors, environmental variability etc. as well as underlying transmission dynamics of the disease is important for epidemiological research on malaria and its eradication. Thus, development of suitable modeling approach and methodology, based on the available data on the incidence of the disease and other related factors is of utmost importance. In this study, we developed a simple non-linear regression methodology in modeling and forecasting malaria incidence in Chennai city, India, and predicted future disease incidence with high confidence level. We considered three types of data to develop the regression methodology: a longer time series data of Slide Positivity Rates (SPR of malaria; a smaller time series data (deaths due to Plasmodium vivax of one year; and spatial data (zonal distribution of P. vivax deaths for the city along with the climatic factors, population and previous incidence of the disease. We performed variable selection by simple correlation study, identification of the initial relationship between variables through non-linear curve fitting and used multi-step methods for induction of variables in the non-linear regression analysis along with applied Gauss-Markov models, and ANOVA for testing the prediction, validity and constructing the confidence intervals. The results execute the applicability of our method for different types of data, the autoregressive nature of forecasting, and show high prediction power for both SPR and P. vivax deaths, where the one-lag SPR values plays an influential role and proves useful for better prediction. Different climatic factors are identified as playing crucial role on shaping the disease curve. Further, disease incidence at zonal level and the effect of causative factors on different zonal clusters indicate the pattern of malaria prevalence in the city

Linear models for joint association and linkage QTL mapping

Directory of Open Access Journals (Sweden)

Fernando Rohan L

2009-09-01

Full Text Available Abstract Background Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure. Results We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided. Conclusion The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.

Non-linear nuclear engineering models as genetic programming application

International Nuclear Information System (INIS)

Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S.

1997-01-01

This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs

Multiple Linear Regression Model Based on Neural Network and Its Application in the MBR Simulation

Directory of Open Access Journals (Sweden)

Chunqing Li

2012-01-01

Full Text Available The computer simulation of the membrane bioreactor MBR has become the research focus of the MBR simulation. In order to compensate for the defects, for example, long test period, high cost, invisible equipment seal, and so forth, on the basis of conducting in-depth study of the mathematical model of the MBR, combining with neural network theory, this paper proposed a three-dimensional simulation system for MBR wastewater treatment, with fast speed, high efficiency, and good visualization. The system is researched and developed with the hybrid programming of VC++ programming language and OpenGL, with a multifactor linear regression model of affecting MBR membrane fluxes based on neural network, applying modeling method of integer instead of float and quad tree recursion. The experiments show that the three-dimensional simulation system, using the above models and methods, has the inspiration and reference for the future research and application of the MBR simulation technology.

Efficient Blind System Identification of Non-Gaussian Auto-Regressive Models with HMM Modeling of the Excitation

DEFF Research Database (Denmark)

Li, Chunjian; Andersen, Søren Vang

2007-01-01

We propose two blind system identification methods that exploit the underlying dynamics of non-Gaussian signals. The two signal models to be identified are: an Auto-Regressive (AR) model driven by a discrete-state Hidden Markov process, and the same model whose output is perturbed by white Gaussi...... outputs. The signal models are general and suitable to numerous important signals, such as speech signals and base-band communication signals. Applications to speech analysis and blind channel equalization are given to exemplify the efficiency of the new methods....

Linear regression methods a ccording to objective functions

OpenAIRE

Yasemin Sisman; Sebahattin Bektas

2012-01-01

The aim of the study is to explain the parameter estimation methods and the regression analysis. The simple linear regressionmethods grouped according to the objective function are introduced. The numerical solution is achieved for the simple linear regressionmethods according to objective function of Least Squares and theLeast Absolute Value adjustment methods. The success of the appliedmethods is analyzed using their objective function values.

Scattering of massless lumps and non-local charges in the two-dimensional classical non-linear sigma-model

International Nuclear Information System (INIS)

Luescher, M.; Pohlmeyer, K.

1977-09-01

Finite energy solutions of the field equations of the non-linear sigma-model are shown to decay asymptotically into massless lumps. By means of a linear eigenvalue problem connected with the field equations we then find an infinite set of dynamical conserved charges. They, however, do not provide sufficient information to decode the complicated scattering of lumps. (orig.) [de

Non-linear dynamics of wind turbine wings

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2006-01-01

The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced...

Non-linear realization of α0 -extended supersymmetry

International Nuclear Information System (INIS)

Nishino, Hitoshi

2000-01-01

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group for arbitrary D and N , which coincides with the linearly supersymmetric Born-Infeld action in D=10 at the lowest order. For the gauge group U(N) for M(atrix)-theory, this model has N 2 -extended non-linear supersymmetries, so that its large N limit corresponds to the infinitely many (α 0 ) supersymmetries. We also perform a duality transformation from F μν into its Hodge dual N μ 1 ctdot μD-2 . We next point out that any Chern-Simons action for any (super)groups has the non-linear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p -brane action with fermionic kappa-symmetry. We further elaborate these results to what we call 'simplified' (Supersymmetry) 2 -models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in 'curved' space-time can be interpreted as 'non-perturbative' effect starting with the 'flat' space-time

Asymptotic analysis of a stochastic non-linear nuclear reactor model

International Nuclear Information System (INIS)

Rodriguez, M.A.; Sancho, J.M.

1986-01-01

The asymptotic behaviour of a stochastic non-linear nuclear reactor modelled by a master equation is analysed in two different limits: the thermodynamic limit and the zero-neutron-source limit. In the first limit a finite steady neutron density is obtained. The second limit predicts the neutron extinction. The interplay between these two limits is studied for different situations. (author)

Testing for marginal linear effects in quantile regression

KAUST Repository

Wang, Huixia Judy

2017-10-23

The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.

Testing for marginal linear effects in quantile regression

KAUST Repository

Wang, Huixia Judy; McKeague, Ian W.; Qian, Min

2017-01-01

The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.

Plateletpheresis efficiency and mathematical correction of software-derived platelet yield prediction: A linear regression and ROC modeling approach.

Science.gov (United States)

Jaime-Pérez, José Carlos; Jiménez-Castillo, Raúl Alberto; Vázquez-Hernández, Karina Elizabeth; Salazar-Riojas, Rosario; Méndez-Ramírez, Nereida; Gómez-Almaguer, David

2017-10-01

Advances in automated cell separators have improved the efficiency of plateletpheresis and the possibility of obtaining double products (DP). We assessed cell processor accuracy of predicted platelet (PLT) yields with the goal of a better prediction of DP collections. This retrospective proof-of-concept study included 302 plateletpheresis procedures performed on a Trima Accel v6.0 at the apheresis unit of a hematology department. Donor variables, software predicted yield and actual PLT yield were statistically evaluated. Software prediction was optimized by linear regression analysis and its optimal cut-off to obtain a DP assessed by receiver operating characteristic curve (ROC) modeling. Three hundred and two plateletpheresis procedures were performed; in 271 (89.7%) occasions, donors were men and in 31 (10.3%) women. Pre-donation PLT count had the best direct correlation with actual PLT yield (r = 0.486. P Simple correction derived from linear regression analysis accurately corrected this underestimation and ROC analysis identified a precise cut-off to reliably predict a DP. © 2016 Wiley Periodicals, Inc.

Implementation of neural network based non-linear predictive

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1998-01-01

The paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems including open loop unstable and non-minimum phase systems, but has also been proposed extended for the control of non......-linear systems. GPC is model-based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis on an efficient Quasi......-Newton optimization algorithm. The performance is demonstrated on a pneumatic servo system....

Enhancement of Visual Field Predictions with Pointwise Exponential Regression (PER) and Pointwise Linear Regression (PLR).

Science.gov (United States)