Generalized Linear Mixed Models

Author: Charles E. McCulloch

Publisher: IMS

ISBN: 9780940600546

Category: Mathematics

Page: 84

View: 9953

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

Generalized Linear Mixed Models

Modern Concepts, Methods and Applications

Author: Walter W. Stroup

Publisher: CRC Press

ISBN: 1439815135

Category: Mathematics

Page: 555

View: 8258

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.

Generalized, Linear, and Mixed Models

Author: Charles E. McCulloch,Shayle R. Searle,John M. Neuhaus

Publisher: John Wiley & Sons

ISBN: 1118209966

Category: Social Science

Page: 424

View: 9547

An accessible and self-contained introduction to statisticalmodels-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Editionprovides an up-to-date treatment of the essential techniques fordeveloping and applying a wide variety of statistical models. Thebook presents thorough and unified coverage of the theory behindgeneralized, linear, and mixed models and highlights theirsimilarities and differences in various construction, application,and computational aspects. A clear introduction to the basic ideas of fixed effects models,random effects models, and mixed models is maintained throughout,and each chapter illustrates how these models are applicable in awide array of contexts. In addition, a discussion of generalmethods for the analysis of such models is presented with anemphasis on the method of maximum likelihood for the estimation ofparameters. The authors also provide comprehensive coverage of thelatest statistical models for correlated, non-normally distributeddata. Thoroughly updated to reflect the latest developments in thefield, the Second Edition features: A new chapter that covers omitted covariates, incorrect randomeffects distribution, correlation of covariates and random effects,and robust variance estimation A new chapter that treats shared random effects models, latentclass models, and properties of models A revised chapter on longitudinal data, which now includes adiscussion of generalized linear models, modern advances inlongitudinal data analysis, and the use between and withincovariate decompositions Expanded coverage of marginal versus conditional models Numerous new and updated examples With its accessible style and wealth of illustrative exercises,Generalized, Linear, and Mixed Models, Second Edition is anideal book for courses on generalized linear and mixed models atthe upper-undergraduate and beginning-graduate levels. It alsoserves as a valuable reference for applied statisticians,industrial practitioners, and researchers.

Multivariate Generalized Linear Mixed Models Using R

Author: Damon Mark Berridge,Robert Crouchley

Publisher: CRC Press

ISBN: 1439813264

Category: Mathematics

Page: 304

View: 468

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.

Linear and Generalized Linear Mixed Models and Their Applications

Author: Jiming Jiang

Publisher: Springer Science & Business Media

ISBN: 0387479465

Category: Mathematics

Page: 257

View: 1534

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 9780203492284

Category: Mathematics

Page: 312

View: 6303

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.

Generalized Linear Models

A Bayesian Perspective

Author: Dipak K. Dey,Sujit K. Ghosh,Bani K. Mallick

Publisher: CRC Press

ISBN: 9780824790349

Category: Mathematics

Page: 440

View: 1926

This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers parametric and semiparametric approaches to overdispersed GLMs, presents methods of analyzing correlated binary data using latent variables. It also proposes a semiparametric method to model link functions for binary response data, and identifies areas of important future research and new applications of GLMs.

Analysis of Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences

Author: Edward Gbur,American Society of Agronomy,Soil Science Society of America,Crop Science Society of America

Publisher: ASA-CSSA-SSSA

ISBN: 9780891181828

Category: Science

Page: 283

View: 4262

Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences provides readers with an understanding and appreciation for the design and analysis of mixed models for non-normally distributed data. It is the only publication of its kind directed specifically toward the agricultural and natural resources sciences audience. Readers will especially benefit from the numerous worked examples based on actual experimental data and the discussion of pitfalls associated with incorrect analyses.

Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials

Author: Toshiro Tango

Publisher: CRC Press

ISBN: 1351648144

Category: Mathematics

Page: 376

View: 3174

Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials is the first book focused on the application of generalized linear mixed models and its related models in the statistical design and analysis of repeated measures from randomized controlled trials. The author introduces a new repeated measures design called S:T design combined with mixed models as a practical and useful framework of parallel group RCT design because of easy handling of missing data and sample size reduction. The book emphasizes practical, rather than theoretical, aspects of statistical analyses and the interpretation of results. It includes chapters in which the author describes some old-fashioned analysis designs that have been in the literature and compares the results with those obtained from the corresponding mixed models. The book will be of interest to biostatisticians, researchers, and graduate students in the medical and health sciences who are involved in clinical trials.

SAS for Mixed Models, Second Edition

Author: Ramon C. Littell, Ph.D.,George A. Milliken, Ph.D.,Walter W. Stroup, Ph.D.,Russell D. Wolfinger, Ph.D.,Oliver Schabenberger, Ph.D.

Publisher: SAS Institute

ISBN: 9781599940786

Category: Mathematics

Page: 828

View: 1975

The indispensable, up-to-date guide to mixed models using SAS. Discover the latest capabilities available for a variety of applications featuring the MIXED, GLIMMIX, and NLMIXED procedures in SAS for Mixed Models, Second Edition, the comprehensive mixed models guide for data analysis, completely revised and updated for SAS 9 by authors Ramon Littell, George Milliken, Walter Stroup, Russell Wolfinger, and Oliver Schabenberger. The theory underlying the models, the forms of the models for various applications, and a wealth of examples from different fields of study are integrated in the discussions of these models: random effect only and random coefficients models; split-plot, multilocation, and repeated measures models; hierarchical models with nested random effects; analysis of covariance models; spatial correlation models; generalized linear mixed models; and nonlinear mixed models. Professionals and students with a background in two-way ANOVA and regression and a basic knowledge of linear models and matrix algebra will benefit from the topics covered. This book is part of the SAS Press program.

Foundations of Linear and Generalized Linear Models

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 1118730038

Category: Mathematics

Page: 444

View: 3980

"This book presents an overview of the foundations and the key ideas and results of linear and generalized linear models under one cover. Written by a prolific academic, researcher, and textbook writer, Foundations of Linear and Generalized Linear Modelsis soon to become the gold standard by which all existing textbooks on the topic will be compared. While the emphasis is clearly and succinctly on theoretical underpinnings, applications in "R" are presented when they help to elucidate the content or promote practical model building. Each chapter contains approximately 15-20 exercises, primarily for readers to practice and extend the theory, but, also to assimilate the ideas by doing some data analysis. The carefully crafted models and examples convey basic concepts and do not get mired down in non-trivial considerations. An author-maintained web site includes, among other numerous pedagogical supplements, analyses that parallel the "R" routines from the book in SAS, SPSS and Stata"--

Generalized Linear Models with Random Effects

Unified Analysis via H-likelihood

Author: Youngjo Lee,John A. Nelder,Yudi Pawitan

Publisher: CRC Press

ISBN: 9781420011340

Category: Mathematics

Page: 416

View: 3033

Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors. Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of which can be run by using the code supplied on the accompanying CD, this book is beneficial to statisticians and researchers involved in the above applications as well as quality-improvement experiments and missing-data analysis.