Non-Standard Problems in Inference for Additive and Linear Mixed Models PDF Download
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Author: Sonja Greven
Publisher: Cuvillier Verlag
ISBN: 3867274916
Category : Inference
Languages : en
Pages : 153
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Book Description
Author: Sonja Greven
Publisher: Cuvillier Verlag
ISBN: 3867274916
Category : Inference
Languages : en
Pages : 153
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Book Description
Author: Daowen Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 342
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Book Description
Author: Simon Wood
Publisher: CRC Press
ISBN: 1584884746
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.
Author: Thomas Kneib
Publisher:
ISBN: 9783899633184
Category :
Languages : en
Pages : 246
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Book Description
Author: Walter W. Stroup
Publisher: SAS Institute
ISBN: 163526152X
Category : Computers
Languages : en
Pages : 608
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Book Description
Discover the power of mixed models with SAS. Mixed models—now the mainstream vehicle for analyzing most research data—are part of the core curriculum in most master’s degree programs in statistics and data science. In a single volume, this book updates both SAS® for Linear Models, Fourth Edition, and SAS® for Mixed Models, Second Edition, covering the latest capabilities for a variety of applications featuring the SAS GLIMMIX and MIXED procedures. Written for instructors of statistics, graduate students, scientists, statisticians in business or government, and other decision makers, SAS® for Mixed Models is the perfect entry for those with a background in two-way analysis of variance, regression, and intermediate-level use of SAS. This book expands coverage of mixed models for non-normal data and mixed-model-based precision and power analysis, including the following topics: Random-effect-only and random-coefficients models Multilevel, split-plot, multilocation, and repeated measures models Hierarchical models with nested random effects Analysis of covariance models Generalized linear mixed models This book is part of the SAS Press program.
Author: Lang Wu
Publisher: CRC Press
ISBN: 9781420074086
Category : Mathematics
Languages : en
Pages : 431
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Book Description
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Author: Javier Prieto Tejedor
Publisher: BoD – Books on Demand
ISBN: 9535135775
Category : Mathematics
Languages : en
Pages : 379
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Book Description
The range of Bayesian inference algorithms and their different applications has been greatly expanded since the first implementation of a Kalman filter by Stanley F. Schmidt for the Apollo program. Extended Kalman filters or particle filters are just some examples of these algorithms that have been extensively applied to logistics, medical services, search and rescue operations, or automotive safety, among others. This book takes a look at both theoretical foundations of Bayesian inference and practical implementations in different fields. It is intended as an introductory guide for the application of Bayesian inference in the fields of life sciences, engineering, and economics, as well as a source document of fundamentals for intermediate Bayesian readers.
Author: Andreas Groll
Publisher: Cuvillier Verlag
ISBN: 3736939639
Category : Business & Economics
Languages : en
Pages : 175
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Book Description
A regression analysis describes the dependency of random variables in the form of a functional relationship. One distinguishes between the dependent response variable and one or more independent influence variables. There is a variety of model classes and inference methods available, ranging from the conventional linear regression model up to recent non- and semiparametric regression models. The so-called generalized regression models form a methodically consistent framework incorporating many regression approaches with response variables that are not necessarily normally distributed, including the conventional linear regression model based on the normal distribution assumption as a special case. When repeated measurements are modeled in addition to fixed effects also random effects or coefficients can be included. Such models are known as Random Effects Models or Mixed Models. As a consequence, regression procedures are applicable extremely versatile and consider very different problems. In this dissertation regularization techniques for generalized mixed models are developed that are able to perform variable selection. These techniques are especially appropriate when many potential influence variables are present and existing approaches tend to fail. First of all a componentwise boosting technique for generalized linear mixed models is presented which is based on the likelihood function and works by iteratively fitting the residuals using weak learners. The complexity of the resulting estimator is determined by information criteria. For the estimation of variance components two approaches are considered, an estimator resulting from maximizing the profile likelihood, and an estimator which can be calculated using an approximative EM-algorithm. Then the boosting concept is extended to mixed models with ordinal response variables. Two different types of ordered models are considered, the threshold model, also known as cumulative model, and the sequential model. Both are based on the assumption that the observed response variable results from a categorized version of a latent metric variable. In the further course of the thesis the boosting approach is extended to additive predictors. The unknown functions to be estimated are expanded in B-spline basis functions, whose smoothness is controlled by penalty terms. Finally, a suitable L1-regularization technique for generalized linear models is presented, which is based on a combination of Fisher scoring and gradient optimization. Extensive simulation studies and numerous applications illustrate the competitiveness of the methods constructed in this thesis compared to conventional approaches. For the calculation of standard errors bootstrap methods are used.
Author: Paul H.C. Eilers
Publisher: Cambridge University Press
ISBN: 1108686885
Category : Computers
Languages : en
Pages : 213
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Book Description
This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers.
Author: Charles E. McCulloch
Publisher: IMS
ISBN: 9780940600546
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models
