1st Edition

Generalized Linear Mixed Models Modern Concepts, Methods and Applications

By Walter W. Stroup Copyright 2012
    555 Pages 85 B/W Illustrations
    by CRC Press

    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.

    PART I The Big Picture
    Modeling Basics
    What Is a Model?
    Two Model Forms: Model Equation and Probability Distribution
    Types of Model Effects
    Writing Models in Matrix Form
    Summary: Essential Elements for a Complete Statement of the Model

    Design Matters
    Introductory Ideas for Translating Design and Objectives into Models
    Describing "Data Architecture" to Facilitate Model Specification
    From Plot Plan to Linear Predictor
    Distribution Matters
    More Complex Example: Multiple Factors with Different Units of Replication

    Setting the Stage
    Goals for Inference with Models: Overview
    Basic Tools of Inference
    Issue I: Data Scale vs. Model Scale
    Issue II: Inference Space
    Issue III: Conditional and Marginal Models
    Summary

    PART II Estimation and Inference Essentials
    Estimation
    Introduction
    Essential Background
    Fixed Effects Only
    Gaussian Mixed Models
    Generalized Linear Mixed Models
    Summary

    Inference, Part I: Model Effects
    Introduction
    Essential Background
    Approaches to Testing
    Inference Using Model-Based Statistics
    Inference Using Empirical Standard Error
    Summary of Main Ideas and General Guidelines for Implementation

    Inference, Part II: Covariance Components
    Introduction
    Formal Testing of Covariance Components
    Fit Statistics to Compare Covariance Models
    Interval Estimation
    Summary

    PART III Working with GLMMs
    Treatment and Explanatory Variable Structure

    Types of Treatment Structures
    Types of Estimable Functions
    Multiple Factor Models: Overview
    Multifactor Models with All Factors Qualitative
    Multifactor: Some Factors Qualitative, Some Factors Quantitative
    Multifactor: All Factors Quantitative
    Summary

    Multilevel Models
    Types of Design Structure: Single- and Multilevel Models Defined
    Types of Multilevel Models and How They Arise
    Role of Blocking in Multilevel Models
    Working with Multilevel Designs
    Marginal and Conditional Multilevel Models
    Summary

    Best Linear Unbiased Prediction
    Review of Estimable and Predictable Functions
    BLUP in Random-Effects-Only Models
    Gaussian Data with Fixed and Random Effects
    Advanced Applications with Complex Z Matrices
    Summary

    Rates and Proportions
    Types of Rate and Proportion Data
    Discrete Proportions: Binary and Binomial Data
    Alternative Link Functions for Binomial Data
    Continuous Proportions
    Summary

    Counts
    Introduction
    Overdispersion in Count Data
    More on Alternative Distributions
    Conditional and Marginal
    Too Many Zeroes
    Summary

    Time-to-Event Data
    Introduction: Probability Concepts for Time-to-Event Data
    Gamma GLMMs
    GLMMs and Survival Analysis
    Summary

    Multinomial Data
    Overview
    Multinomial Data with Ordered Categories
    Nominal Categories: Generalized Logit Models
    Model Comparison
    Summary

    Correlated Errors, Part I: Repeated Measures
    Overview
    Gaussian Data: Correlation and Covariance Models for LMMs
    Covariance Model Selection
    Non-Gaussian Case
    Issues for Non-Gaussian Repeated Measures
    Summary

    Correlated Errors, Part II: Spatial Variability
    Overview
    Gaussian Case with Covariance Model
    Spatial Covariance Modeling by Smoothing Spline
    Non-Gaussian Case
    Summary

    Power, Sample Size, and Planning
    Basics of GLMM-Based Power and Precision Analysis
    Gaussian Example
    Power for Binomial GLMMs
    GLMM-Based Power Analysis for Count Data
    Power and Planning for Repeated Measures
    Summary

    Appendices

    References

    Index

    Biography

    Walter W. Stroup

    "The book focuses on data-driven modeling and design processes, and it provides a context for extending traditional linear model thinking to generalised linear mixed modeling. This is a very sound text which teachers of any course on GLMMs should consider adopting."
    —Erkki P. Liski, International Statistical Review (2013), 81

    "Walter Stroup is a leading authority on GLMMs for applied statisticians, especially as implemented in the SAS programming environment. He offers a thorough, engaging, and opinionated treatment of the subject … I found the ‘fully general’ GLMM approach to modeling and design issues (Chapters 1 and 2) to be quite illuminating. … it is best to use this text in conjunction with SAS. Prospective readers without current access to SAS will be pleased to know that a reasonable level of access to SAS is now available at no cost to students and teachers on the web … If the reader prefers to work with GLMMs in the free, powerful, and state-of-the-art R environment, then he/she should supplement this text with some others that are built around R. I myself had good luck using Stroup’s text along with Julian Faraway’s two books Linear Models with R and Expanding the Linear Model with R, both published by CRC Press."
    —Homer White, MAA Reviews, June 2013

    "… for SAS users concerned with the analysis of trials, it is a very good resource. There are excellent discussions on many important concepts such as likelihood ratio testing and model selection criteria. PROC GLIMMIX is a powerful procedure implementing the rich family of GLMMs, and this book gives coverage to a wide variety of models with ample software illustration."
    —Gillian Z. Heller, Australian & New Zealand Journal of Statistics, 2013