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

555 Pages
by CRC Press

Also available as eBook on:

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