Linear Mixed Models

A Practical Guide Using Statistical Software, Second Edition

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Author: Brady T. West,Kathleen B. Welch,Andrzej T Galecki

Publisher: CRC Press

ISBN: 1466560991

Category: Mathematics

Page: 440

View: 5877

Highly recommended by JASA, Technometrics, and other journals, the first edition of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition continues to lead readers step by step through the process of fitting LMMs. This second edition covers additional topics on the application of LMMs that are valuable for data analysts in all fields. It also updates the case studies using the latest versions of the software procedures and provides up-to-date information on the options and features of the software procedures available for fitting LMMs in SAS, SPSS, Stata, R/S-plus, and HLM. New to the Second Edition A new chapter on models with crossed random effects that uses a case study to illustrate software procedures capable of fitting these models Power analysis methods for longitudinal and clustered study designs, including software options for power analyses and suggested approaches to writing simulations Use of the lmer() function in the lme4 R package New sections on fitting LMMs to complex sample survey data and Bayesian approaches to making inferences based on LMMs Updated graphical procedures in the software packages Substantially revised index to enable more efficient reading and easier location of material on selected topics or software options More practical recommendations on using the software for analysis A new R package (WWGbook) that contains all of the data sets used in the examples Ideal for anyone who uses software for statistical modeling, this book eliminates the need to read multiple software-specific texts by covering the most popular software programs for fitting LMMs in one handy guide. The authors illustrate the models and methods through real-world examples that enable comparisons of model-fitting options and results across the software procedures.

Linear Mixed Models

A Practical Guide Using Statistical Software, Second Edition

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Author: Brady T. West,Kathleen B. Welch,Andrzej T Galecki

Publisher: CRC Press

ISBN: 1466561025

Category: Mathematics

Page: 440

View: 6722

Highly recommended by JASA, Technometrics, and other journals, the first edition of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition continues to lead readers step by step through the process of fitting LMMs. This second edition covers additional topics on the application of LMMs that are valuable for data analysts in all fields. It also updates the case studies using the latest versions of the software procedures and provides up-to-date information on the options and features of the software procedures available for fitting LMMs in SAS, SPSS, Stata, R/S-plus, and HLM. New to the Second Edition A new chapter on models with crossed random effects that uses a case study to illustrate software procedures capable of fitting these models Power analysis methods for longitudinal and clustered study designs, including software options for power analyses and suggested approaches to writing simulations Use of the lmer() function in the lme4 R package New sections on fitting LMMs to complex sample survey data and Bayesian approaches to making inferences based on LMMs Updated graphical procedures in the software packages Substantially revised index to enable more efficient reading and easier location of material on selected topics or software options More practical recommendations on using the software for analysis A new R package (WWGbook) that contains all of the data sets used in the examples Ideal for anyone who uses software for statistical modeling, this book eliminates the need to read multiple software-specific texts by covering the most popular software programs for fitting LMMs in one handy guide. The authors illustrate the models and methods through real-world examples that enable comparisons of model-fitting options and results across the software procedures.

Linear Mixed Models

A Practical Guide Using Statistical Software

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Author: Brady T. West,Kathleen B. Welch,Andrzej T Galecki

Publisher: CRC Press

ISBN: 1420010433

Category: Mathematics

Page: 376

View: 3867

Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM. The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on both general and hierarchical model specifications, develop the model-building process step-by-step, and demonstrate the estimation, testing, and interpretation of fixed-effect parameters and covariance parameters associated with random effects. These concepts are illustrated through examples using real-world data sets that enable comparisons of model fitting options and results across the software procedures. The book also gives an overview of important options and features available in each procedure. Making popular software procedures for fitting LMMs easy-to-use, this valuable resource shows how to perform LMM analyses and provides a clear explanation of mixed modeling techniques and theories.

Generalized Linear Mixed Models

Modern Concepts, Methods and Applications

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Author: Walter W. Stroup

Publisher: CRC Press

ISBN: 1439815135

Category: Mathematics

Page: 555

View: 9844

Generalized Linear Mixed Models: Modern Concepts, Methods and Applications presents an introduction to linear modeling using the generalized linear mixed model (GLMM) as an overarching conceptual framework. For readers new to linear models, the book helps them see the big picture. It shows how linear models fit with the rest of the core statistics curriculum and points out the major issues that statistical modelers must consider. Along with describing common applications of GLMMs, the text introduces the essential theory and main methodology associated with linear models that accommodate random model effects and non-Gaussian data. Unlike traditional linear model textbooks that focus on normally distributed data, this one adopts a generalized mixed model approach throughout: data for linear modeling need not be normally distributed and effects may be fixed or random. With numerous examples using SAS® PROC GLIMMIX, this book is ideal for graduate students in statistics, statistics professionals seeking to update their knowledge, and researchers new to the generalized linear model thought process. It focuses on data-driven processes and provides context for extending traditional linear model thinking to generalized linear mixed modeling. See Professor Stroup discuss the book.

Mixed-Effects Models in S and S-PLUS

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Author: José C. Pinheiro,Douglas Bates

Publisher: Springer Science & Business Media

ISBN: 1441903178

Category: Computers

Page: 530

View: 8564

R, linear models, random, fixed, data, analysis, fit.

Linear Mixed-Effects Models Using R

A Step-by-Step Approach

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Author: Andrzej Gałecki,Tomasz Burzykowski

Publisher: Springer Science & Business Media

ISBN: 1461439000

Category: Mathematics

Page: 542

View: 6517

Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.

Mixed Models

Theory and Applications with R

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Author: Eugene Demidenko

Publisher: John Wiley & Sons

ISBN: 1118091574

Category: Mathematics

Page: 717

View: 1914

Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. The new edition includes significant updating, over 300 exercises, stimulating chapter projects and model simulations, inclusion of R subroutines, and a revised text format. The target audience continues to be graduate students and researchers. An author-maintained web site is available with solutions to exercises and a compendium of relevant data sets.

Mixed Effects Models for Complex Data

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Author: Lang Wu

Publisher: CRC Press

ISBN: 9781420074086

Category: Mathematics

Page: 431

View: 2137

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.

Generalized Additive Models

An Introduction with R, Second Edition

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Author: Simon N. Wood

Publisher: CRC Press

ISBN: 1498728375

Category: Mathematics

Page: 496

View: 8030

The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models. The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study. Simon N. Wood is a professor of Statistical Science at the University of Bristol, UK, and author of the R package mgcv.

Multivariate Generalized Linear Mixed Models Using R

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Author: Damon Mark Berridge,Robert Crouchley

Publisher: CRC Press

ISBN: 1439813272

Category: Mathematics

Page: 304

View: 4047

Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R. A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model estimation, and endogenous variables, along with SabreR commands and examples. Improve Your Longitudinal Study In medical and social science research, MGLMMs help disentangle state dependence from incidental parameters. Focusing on these sophisticated data analysis techniques, this book explains the statistical theory and modeling involved in longitudinal studies. Many examples throughout the text illustrate the analysis of real-world data sets. Exercises, solutions, and other material are available on a supporting website.

Statistical Design and Analysis of Stability Studies

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Author: Shein-Chung Chow

Publisher: CRC Press

ISBN: 9781584889069

Category: Mathematics

Page: 352

View: 5468

The US Food and Drug Administration's Report to the Nation in 2004 and 2005 indicated that one of the top reasons for drug recall was that stability data did not support existing expiration dates. Pharmaceutical companies conduct stability studies to characterize the degradation of drug products and to estimate drug shelf life. Illustrating how stability studies play an important role in drug safety and quality assurance, Statistical Design and Analysis of Stability Studies presents the principles and methodologies in the design and analysis of stability studies. After introducing the basic concepts of stability testing, the book focuses on short-term stability studies and reviews several methods for estimating drug expiration dating periods. It then compares some commonly employed study designs and discusses both fixed and random batch statistical analyses. Following a chapter on the statistical methods for stability analysis under a linear mixed effects model, the book examines stability analyses with discrete responses, multiple components, and frozen drug products. In addition, the author provides statistical methods for dissolution testing and explores current issues and recent developments in stability studies. To ensure the safety of consumers, professionals in the field must carry out stability studies to determine the reliability of drug products during their expiration period. This book provides the material necessary for you to perform stability designs and analyses in pharmaceutical research and development.

Applied Survey Data Analysis, Second Edition

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Author: Steven G. Heeringa,Brady T. West,Patricia A. Berglund

Publisher: CRC Press

ISBN: 1351649302

Category: Mathematics

Page: 590

View: 3611

Highly recommended by the Journal of Official Statistics, The American Statistician, and other journals, Applied Survey Data Analysis, Second Edition provides an up-to-date overview of state-of-the-art approaches to the analysis of complex sample survey data. Building on the wealth of material on practical approaches to descriptive analysis and regression modeling from the first edition, this second edition expands the topics covered and presents more step-by-step examples of modern approaches to the analysis of survey data using the newest statistical software. Designed for readers working in a wide array of disciplines who use survey data in their work, this book continues to provide a useful framework for integrating more in-depth studies of the theory and methods of survey data analysis. An example-driven guide to the applied statistical analysis and interpretation of survey data, the second edition contains many new examples and practical exercises based on recent versions of real-world survey data sets. Although the authors continue to use Stata for most examples in the text, they also continue to offer SAS, SPSS, SUDAAN, R, WesVar, IVEware, and Mplus software code for replicating the examples on the book’s updated website.

Generalized Linear and Nonlinear Models for Correlated Data

Theory and Applications Using SAS

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Author: Edward F. Vonesh

Publisher: SAS Institute

ISBN: 1612900917

Category: MATHEMATICS

Page: 549

View: 7049

Edward F. Vonesh's "Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS" is devoted to the analysis of correlated response data using SAS, with special emphasis on applications that require the use of generalized linear models or generalized nonlinear models. Written in a clear, easy-to-understand manner, it provides applied statisticians with the necessary theory, tools, and understanding to conduct complex analyses of continuous and/or discrete correlated data in a longitudinal or clustered data setting. Using numerous and complex examples, the book emphasizes real-world applications where the underlying model requires a nonlinear rather than linear formulation and compares and contrasts the various estimation techniques for both marginal and mixed-effects models. The SAS procedures MIXED, GENMOD, GLIMMIX, and NLMIXED as well as user-specified macros will be used extensively in these applications. In addition, the book provides detailed software code with most examples so that readers can begin applying the various techniques immediately.

Data Analysis Using Hierarchical Generalized Linear Models with R

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Author: Youngjo Lee,Lars Ronnegard,Maengseok Noh

Publisher: CRC Press

ISBN: 135181155X

Category: Mathematics

Page: 322

View: 7388

Since their introduction, hierarchical generalized linear models (HGLMs) have proven useful in various fields by allowing random effects in regression models. Interest in the topic has grown, and various practical analytical tools have been developed. This book summarizes developments within the field and, using data examples, illustrates how to analyse various kinds of data using R. It provides a likelihood approach to advanced statistical modelling including generalized linear models with random effects, survival analysis and frailty models, multivariate HGLMs, factor and structural equation models, robust modelling of random effects, models including penalty and variable selection and hypothesis testing. This example-driven book is aimed primarily at researchers and graduate students, who wish to perform data modelling beyond the frequentist framework, and especially for those searching for a bridge between Bayesian and frequentist statistics.

Linear Mixed Models for Longitudinal Data

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Author: Geert Verbeke,Geert Molenberghs

Publisher: Springer Science & Business Media

ISBN: 1441903003

Category: Mathematics

Page: 570

View: 2073

This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Most analyses were done with the MIXED procedure of the SAS software package, but the data analyses are presented in a software-independent fashion.

The R Book

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Author: Michael J. Crawley

Publisher: John Wiley & Sons

ISBN: 1118448960

Category: Mathematics

Page: 1080

View: 9323

Hugely successful and popular text presenting an extensive and comprehensive guide for all R users The R language is recognized as one of the most powerful and flexible statistical software packages, enabling users to apply many statistical techniques that would be impossible without such software to help implement such large data sets. R has become an essential tool for understanding and carrying out research. This edition: Features full colour text and extensive graphics throughout. Introduces a clear structure with numbered section headings to help readers locate information more efficiently. Looks at the evolution of R over the past five years. Features a new chapter on Bayesian Analysis and Meta-Analysis. Presents a fully revised and updated bibliography and reference section. Is supported by an accompanying website allowing examples from the text to be run by the user. Praise for the first edition: ‘…if you are an R user or wannabe R user, this text is the one that should be on your shelf. The breadth of topics covered is unsurpassed when it comes to texts on data analysis in R.’ (The American Statistician, August 2008) ‘The High-level software language of R is setting standards in quantitative analysis. And now anybody can get to grips with it thanks to The R Book…’ (Professional Pensions, July 2007)

Probability and Statistical Inference

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Author: Robert Bartoszynski,Magdalena Niewiadomska-Bugaj

Publisher: John Wiley & Sons

ISBN: 9780470191583

Category: Mathematics

Page: 672

View: 7257

Now updated in a valuable new edition—this user-friendly book focuses on understanding the "why" of mathematical statistics Probability and Statistical Inference, Second Edition introduces key probability and statis-tical concepts through non-trivial, real-world examples and promotes the developmentof intuition rather than simple application. With its coverage of the recent advancements in computer-intensive methods, this update successfully provides the comp-rehensive tools needed to develop a broad understanding of the theory of statisticsand its probabilistic foundations. This outstanding new edition continues to encouragereaders to recognize and fully understand the why, not just the how, behind the concepts,theorems, and methods of statistics. Clear explanations are presented and appliedto various examples that help to impart a deeper understanding of theorems and methods—from fundamental statistical concepts to computational details. Additional features of this Second Edition include: A new chapter on random samples Coverage of computer-intensive techniques in statistical inference featuring Monte Carlo and resampling methods, such as bootstrap and permutation tests, bootstrap confidence intervals with supporting R codes, and additional examples available via the book's FTP site Treatment of survival and hazard function, methods of obtaining estimators, and Bayes estimating Real-world examples that illuminate presented concepts Exercises at the end of each section Providing a straightforward, contemporary approach to modern-day statistical applications, Probability and Statistical Inference, Second Edition is an ideal text for advanced undergraduate- and graduate-level courses in probability and statistical inference. It also serves as a valuable reference for practitioners in any discipline who wish to gain further insight into the latest statistical tools.

Analysis of Clinical Trials Using SAS

A Practical Guide

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Author: Alex Dmitrienko,Geert Molenberghs,Christy Chuang-Stein,Walter W. Offen

Publisher: SAS Institute

ISBN: 9781590477809

Category: Mathematics

Page: 430

View: 9520

In Analysis of Clinical Trials Using SAS: A Practical Guide, Alex Dmitrienko, Geert Molenberghs, Christy Chuang-Stein, and Walter Offen bridge the gap between modern statistical methodology and real-world clinical trial applications. Step-by-step instructions illustrated with examples from actual trials and case studies serve to define a statistical method and its relevance in a clinical trials setting and to illustrate how to implement the method rapidly and efficiently using the power of SAS software. Topics reflect the International Conference on Harmonization (ICH) guidelines for the pharmaceutical industry and address important statistical problems encountered in clinical trials, including analysis of stratified data, incomplete data, multiple inferences, issues arising in safety and efficacy monitoring, and reference intervals for extreme safety and diagnostic measurements. Clinical statisticians, research scientists, and graduate students in biostatistics will greatly benefit from the decades of clinical research experience compiled in this book. Numerous ready-to-use SAS macros and example code are included. This book is part of the SAS Press program.

Statistical Rethinking

A Bayesian Course with Examples in R and Stan

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Author: Richard McElreath

Publisher: CRC Press

ISBN: 1315362619

Category: Mathematics

Page: 487

View: 7900

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.