Generalized Linear Mixed Models

Modern Concepts, Methods and Applications

By Walter W. Stroup

© 2012 – CRC Press

555 pages | 85 B/W Illus.

Purchasing Options:
Hardback: 9781439815120
pub: 2012-09-24
US Dollars$93.95

Comp Exam Copy

About the Book

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.


"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

Table of Contents

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


PART II Estimation and Inference Essentials



Essential Background

Fixed Effects Only

Gaussian Mixed Models

Generalized Linear Mixed Models


Inference, Part I: Model Effects


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


Formal Testing of Covariance Components

Fit Statistics to Compare Covariance Models

Interval Estimation


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


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


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


Rates and Proportions

Types of Rate and Proportion Data

Discrete Proportions: Binary and Binomial Data

Alternative Link Functions for Binomial Data

Continuous Proportions




Overdispersion in Count Data

More on Alternative Distributions

Conditional and Marginal

Too Many Zeroes


Time-to-Event Data

Introduction: Probability Concepts for Time-to-Event Data

Gamma GLMMs

GLMMs and Survival Analysis


Multinomial Data


Multinomial Data with Ordered Categories

Nominal Categories: Generalized Logit Models

Model Comparison


Correlated Errors, Part I: Repeated Measures


Gaussian Data: Correlation and Covariance Models for LMMs

Covariance Model Selection

Non-Gaussian Case

Issues for Non-Gaussian Repeated Measures


Correlated Errors, Part II: Spatial Variability


Gaussian Case with Covariance Model

Spatial Covariance Modeling by Smoothing Spline

Non-Gaussian Case


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





About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General