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.
This book discusses advanced statistical methods that can be used to analyse ecological data. Most environmental collected data are measured repeatedly over time, or space and this requires the use of GLMM or GAMM methods. The book starts by revising regression, additive modelling, GAM and GLM, and then discusses dealing with spatial or temporal dependencies and nested data.
This volume presents theoretical developments, applications and computational methods for the analysis and modeling in behavioral and social sciences where data are usually complex to explore and investigate. The challenging proposals provide a connection between statistical methodology and the social domain with particular attention to computational issues in order to effectively address complicated data analysis problems. The papers in this volume stem from contributions initially presented at the joint international meeting JCS-CLADAG held in Anacapri (Italy) where the Japanese Classification Society and the Classification and Data Analysis Group of the Italian Statistical Society had a stimulating scientific discussion and exchange.
Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.
Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.
Wide-Ranging Coverage of Parametric Modeling in Linear and Nonlinear Mixed Effects Models Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools presents a rigorous framework for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time. Easy-to-Use Techniques and Tools for Real-World Data Modeling The book first shows how the framework allows model representation for different data types, including continuous, categorical, count, and time-to-event data. This leads to the use of generic methods, such as the stochastic approximation of the EM algorithm (SAEM), for modeling these diverse data types. The book also covers other essential methods, including Markov chain Monte Carlo (MCMC) and importance sampling techniques. The author uses publicly available software tools to illustrate modeling tasks. Methods are implemented in Monolix, and models are visually explored using Mlxplore and simulated using Simulx. Careful Balance of Mathematical Representation and Practical Implementation This book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Statisticians and mathematicians will appreciate the rigorous representation of the models and theoretical properties of the methods while modelers will welcome the practical capabilities of the tools. The book is also useful for training and teaching in any field where population modeling occurs.
When data consist of grouped observations or clusters, and there is a risk that measurements within the same group are not independent, group-specific random effects can be added to a regression model in order to account for such within-group associations. Regression models that contain such group-specific random effects are called mixed-effects regression models, or simply mixed models. Mixed models are a versatile tool that can handle both balanced and unbalanced datasets and that can also be applied when several layers of grouping are present in the data; these layers can either be nested or crossed. In linguistics, as in many other fields, the use of mixed models has gained ground rapidly over the last decade. This methodological evolution enables us to build more sophisticated and arguably more realistic models, but, due to its technical complexity, also introduces new challenges. This volume brings together a number of promising new evolutions in the use of mixed models in linguistics, but also addresses a number of common complications, misunderstandings, and pitfalls. Topics that are covered include the use of huge datasets, dealing with non-linear relations, issues of cross-validation, and issues of model selection and complex random structures. The volume features examples from various subfields in linguistics. The book also provides R code for a wide range of analyses.
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.
Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.
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.
A Practical Guide Using Statistical Software, Second Edition
Author: Brady T. West
Publisher: CRC Press
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.
Edward 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. This book is part of the SAS Press program.
Carry out a variety of advanced statistical analyses including generalized additive models, mixed effects models, multiple imputation, machine learning, and missing data techniques using R. Each chapter starts with conceptual background information about the techniques, includes multiple examples using R to achieve results, and concludes with a case study. Written by Matt and Joshua F. Wiley, Advanced R Statistical Programming and Data Models shows you how to conduct data analysis using the popular R language. You’ll delve into the preconditions or hypothesis for various statistical tests and techniques and work through concrete examples using R for a variety of these next-level analytics. This is a must-have guide and reference on using and programming with the R language. What You’ll Learn Conduct advanced analyses in R including: generalized linear models, generalized additive models, mixed effects models, machine learning, and parallel processing Carry out regression modeling using R data visualization, linear and advanced regression, additive models, survival / time to event analysis Handle machine learning using R including parallel processing, dimension reduction, and feature selection and classification Address missing data using multiple imputation in R Work on factor analysis, generalized linear mixed models, and modeling intraindividual variability Who This Book Is For Working professionals, researchers, or students who are familiar with R and basic statistical techniques such as linear regression and who want to learn how to use R to perform more advanced analytics. Particularly, researchers and data analysts in the social sciences may benefit from these techniques. Additionally, analysts who need parallel processing to speed up analytics are given proven code to reduce time to result(s).
The generalised linear mixed models (GLMM) is one of the most important tools for analysing clustered data. One of the main feature of clustered data is observational units within the same cluster are correlated, though observational units from different clusters may be independent. The random effects in the GLMM are used to model this correlation.The random effects in the GLMM are unobservable. Writing down an exact expression for the marginal likelihood from the GLMM involves a high dimensional integral and so is intractable when the dimension of the random effects is large.There are two different approaches to handle this problem in the literature. First, approximate the integral directly by the Laplace’s method (Breslow and Clayton, 1993; Pinheiro and Chao, 2006). Secondly, approximate the integrand or joint density by the lower dimensional object such as the product of marginal density or conditional density. This is also called the pseudo-likelihood estimation (Besag, 1974). Typically, one cannot even write down the marginal likelihood explicitly. So the Laplace’s method doesn’t apply here. But one can still use the pseudo-likelihood. Under various regularity conditions, the consistency and asymptotic normality of the pseudo-likelihood estimator have been established using generalised estimating equations (GEE). There are many ways to construct the pseudo-likelihood (Lindsay,1988; Varin et al., 2011). In this thesis, I work exclusively with the pairwise composite likelihood as it is the simplest pseudo-likelihood construction that still captures the pairwise correlation structure. I am interested in the weighted pairwise composite likelihood under complex sampling. Complex sampling is typically informative (Pfeffermann, 1996). One has to add weights in the pairwise likelihood to account for informative sampling, usually chosen to be the inverse sampling inclusion probability. Rao et al. (2013); Yiet al. (2016) considered the weighted pairwise likelihood for two-stage samples in the special case when the sampling clusters are the model clusters. They established consistency of the weighted pairwise composite likelihood estimator and suggested a variance estimator. In this thesis, I continue the study of the weighted pairwise composite likelihood estimator in complex sampling initiated in Rao et al. (2013); Yi et al. (2016). More precisely, my goal is to extend the asymptotic results of the weighted pairwise likelihood estimators to the case when the sampling clusters are not the same as the model clusters. In particular, the consistency and asymptotic normality of the weighted pairwise likelihood estimator are established. Furthermore, I show the empirical variance estimator is consistent. This is surprisingly more difficult than it first seems. It is complicated by the structure of the sampling design, where pairs in the same model clusters might not be in the same sampling clusters. I present simulation results examining the performance of the weighted pairwise likelihood estimators for a random intercept model and a random slope model under various two-stage sampling designs. Finally, the random effects in the mixed model could potentially be correlated as in spatial statistics. My goal in here is to keep extending the asymptotic properties of the weighted pairwise composite likelihood estimator under the Mat ́ern spatial random intercept model. More precisely, I establish consistency and asymptotic normality of the weighted pairwise likelihood estimator under that setting.
Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.