Linear and Generalized Linear Mixed Models and Their Applications

Author: Jiming Jiang
Publisher: Springer Science & Business Media
ISBN: 9780387479460
Release Date: 2007-05-30
Genre: Mathematics

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.

Correlated Data Analysis Modeling Analytics and Applications

Author: Xue-Kun Song
Publisher: Springer Science & Business Media
ISBN: 9780387713922
Release Date: 2007-07-27
Genre: Mathematics

This book covers recent developments in correlated data analysis, using the class of dispersion models as marginal components in the formulation of joint models for correlated data. Much new material is covered here that you won’t find elsewhere.

Correlated Data Analysis Modeling Analytics and Applications

Author: Peter X. -K. Song
Publisher: Springer Science & Business Media
ISBN: 9780387713939
Release Date: 2007-06-30
Genre: Mathematics

This book covers recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to cover a broader range of data types than the traditional generalized linear models. The reader is provided with a systematic treatment for the topic of estimating functions, and both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to the discussions on marginal models and mixed-effects models, this book covers new topics on joint regression analysis based on Gaussian copulas.

Linear Mixed Models for Longitudinal Data

Author: Geert Verbeke
Publisher: Springer Science & Business Media
ISBN: 9781441903006
Release Date: 2009-05-12
Genre: Mathematics

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.

Linear Models with R Second Edition

Author: Julian J. Faraway
Publisher: CRC Press
ISBN: 9781439887349
Release Date: 2016-04-19
Genre: Mathematics

A Hands-On Way to Learning Data Analysis Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Linear Models

Author: Calyampudi R. Rao
Publisher: Springer Science & Business Media
ISBN: 9780387227528
Release Date: 2006-04-06
Genre: Mathematics

An up-to-date account of the theory and applications of linear models, for use as a textbook in statistics at graduate level as well as an accompanying text for other courses in which linear models play a part. The authors present a unified theory of inference from linear models with minimal assumptions, not only through least squares theory, but also using alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights include: - a special emphasis on sensitivity analysis and model selection; - a chapter devoted to the analysis of categorical data based on logic, loglinear, and logistic regression models; - a chapter devoted to incomplete data sets; - an extensive appendix on matrix theory; - a chapter devoted to the analysis of categorical data based on a unified presentation of generalized linear models including GEE-methods for correlated response; - a chapter devoted to incomplete data sets including regression diagnostics to identify Non-MCAR-processes The material covered is thus invaluable not only to graduates, but also to researchers and consultants in statistics.

Bayesian and Frequentist Regression Methods

Author: Jon Wakefield
Publisher: Springer Science & Business Media
ISBN: 9781441909251
Release Date: 2013-01-04
Genre: Mathematics

Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

Linear Mixed Effects Models Using R

Author: Andrzej Gałecki
Publisher: Springer Science & Business Media
ISBN: 9781461439004
Release Date: 2013-02-05
Genre: Mathematics

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.

Statistics for High Dimensional Data

Author: Peter Bühlmann
Publisher: Springer Science & Business Media
ISBN: 9783642201929
Release Date: 2011-06-08
Genre: Mathematics

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

Models for Discrete Longitudinal Data

Author: Geert Molenberghs
Publisher: Springer Science & Business Media
ISBN: 0387251448
Release Date: 2005-08-04
Genre: Mathematics

This book provides a comprehensive treatment on modeling approaches for non-Gaussian repeated measures, possibly subject to incompleteness. The authors begin with models for the full marginal distribution of the outcome vector. This allows model fitting to be based on maximum likelihood principles, immediately implying inferential tools for all parameters in the models. At the same time, they formulate computationally less complex alternatives, including generalized estimating equations and pseudo-likelihood methods. They then briefly introduce conditional models and move on to the random-effects family, encompassing the beta-binomial model, the probit model and, in particular the generalized linear mixed model. Several frequently used procedures for model fitting are discussed and differences between marginal models and random-effects models are given attention The authors consider a variety of extensions, such as models for multivariate longitudinal measurements, random-effects models with serial correlation, and mixed models with non-Gaussian random effects. They sketch the general principles for how to deal with the commonly encountered issue of incomplete longitudinal data. The authors critique frequently used methods and propose flexible and broadly valid methods instead, and conclude with key concepts of sensitivity analysis. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The text is organized so the reader can skip the software-oriented chapters and sections without breaking the logical flow. Geert Molenberghs is Professor of Biostatistics at the Universiteit Hasselt in Belgium and has published methodological work on surrogate markers in clinical trials, categorical data, longitudinal data analysis, and the analysis of non-response in clinical and epidemiological studies. He served as Joint Editor for Applied Statistics (2001–2004) and as Associate Editor for several journals, including Biometrics and Biostatistics. He was President of the International Biometric Society (2004–2005). He was elected Fellow of the American Statistical Association and received the Guy Medal in Bronze from the Royal Statistical Society. Geert Verbeke is Professor of Biostatistics at the Biostatistical Centre of the Katholieke Universiteit Leuven in Belgium. He has published a number of methodological articles on various aspects of models for longitudinal data analyses, with particular emphasis on mixed models. Geert Verbeke is Past President of the Belgian Region of the International Biometric Society, International Program Chair for the International Biometric Conference in Montreal (2006), and Joint Editor of the Journal of the Royal Statistical Society, Series A (2005–2008). He has served as Associate Editor for several journals including Biometrics and Applied Statistics. The authors also wrote a monograph on linear mixed models for longitudinal data (Springer, 2000) and received the American Statistical Association's Excellence in Continuing Education Award, based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.

Vector Generalized Linear and Additive Models

Author: Thomas W. Yee
Publisher: Springer
ISBN: 9781493928187
Release Date: 2015-09-11
Genre: Mathematics

This book presents a greatly enlarged statistical framework compared to generalized linear models (GLMs) with which to approach regression modelling. Comprising of about half-a-dozen major classes of statistical models, and fortified with necessary infrastructure to make the models more fully operable, the framework allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. However, GLMs are not flexible enough to cope with the demands of practical data analysis. And data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. The methodology here and accompanying software (the extensive VGAM R package) are directed at these limitations and are described comprehensively for the first time in one volume. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users. In the second part of the book, the R package VGAM allows readers to grasp immediately applications of the methodology. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences. The methodological contribution of this book stands alone and does not require use of the VGAM package.

Mixed Effects Models in S and S PLUS

Author: José C. Pinheiro
Publisher: Springer Science & Business Media
ISBN: 9781441903174
Release Date: 2009-04-15
Genre: Computers

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

Dynamic Mixed Models for Familial Longitudinal Data

Author: Brajendra C. Sutradhar
Publisher: Springer Science & Business Media
ISBN: 1441983422
Release Date: 2011-01-27
Genre: Mathematics

This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models. This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing ‘working’ correlations based GEE (generalized estimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up. The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents the illustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University Research Professor at Memorial University in St. John’s, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for society’s annual meetings.

A Primer on Linear Models

Author: John F. Monahan
Publisher: CRC Press
ISBN: 1420062042
Release Date: 2008-03-31
Genre: Mathematics

A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Large Sample Techniques for Statistics

Author: Jiming Jiang
Publisher: Springer Science & Business Media
ISBN: 9781441968272
Release Date: 2010-06-30
Genre: Mathematics

In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).