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Publisher:

Chapman & Hall/CRC

Publication Date:

2013

Number of Pages:

529

Format:

Hardcover

Series:

Texts in Statistical Science

Price:

89.95

ISBN:

9781439815120

Category:

Textbook

[Reviewed by , on ]

Homer White

06/10/2013

Walter Stroup is a leading authority on generalized linear mixed models (GLMMs) for applied statisticians, especially as implemented in the SAS programming environment. He offers here a thorough, engaging and opinionated treatment of the subject, one that he says is directed to “graduate students in statistics, statistics professionals seeking to get up to speed, and researchers new to the generalized linear model thought process.”

Most people learn regression modeling in a sequence of steps that more or less increase in generality:

- linear regression and one and two-way ANOVA;
- the revelation that the procedures in Item 1 are special cases of something called the “general linear model”;
- logistic, Poisson, binomial regression, etc.;
- the further revelation that the procedures in items 2 and 3 are all special cases of something called the “generalized linear model”;
- introduction of the notion of random effects, as opposed to the fixed effects that constituted the predictor variables in Items 1-5 above;
- integration of fixed and random effects, producing “generalized linear mixed models”.

Stroup thinks that the time for this sequenced approach has passed. The distinctive feature of this book, therefore, is that it goes for full generality right from the start. Stroup believes that early awareness of the full GLMM picture will help the working statistician improve his/her ability to understand issues in experimental design and statistical modeling, even in those cases where GLMM in its fullness is not required.

Accordingly the book begins with ground-up treatments of the concept of a statistical model (Chapter One, Modeling Basics) and the design of experiments and studies (Chapter Two, Design Matters). An especially illuminating feature of Chapter Two is the author’s distinction between two techniques for moving from a study design to the construction of an appropriate linear predictor, namely: the “unit of replication” approach and the WWFD (What Would Fisher Do) approach. Chapter Three introduces the basic tools of statistical inference in GLMMs: parameter estimation and hypothesis testing.

All readers should grapple with Chapters 1–3. Readers interested in learning more of the background theory behind the inferential procedures will want to study Chapters 4–6.

Chapters 7–9 cover topics that prepare the reader for specific applications in Chapters 10–16. These later chapters — addressing rates and proportions, count data, time-to-event data, multinomial categorical and ordinal data, repeated measures and spatial variability — clearly are the manna of the text. It appears possible to jump into most of the topics in Chapters 10–16 after a perusal of Chapters 1 through 3 — I tried a bit of that myself — but at some points a study of portions of Chapters 7, 8 and 9 is necessary for full understanding and responsible use of the procedure of interest.

How well does the book succeed in its stated purpose? My own evaluation is based on my status as someone in between a “statistics professional trying to get up to speed” and a “researcher new to the generalized linear model thought process.” I found the “fully general “ GLMM approach to modeling and design issues (Chapters 1 and 2) to be quite illuminating. However, I am not sure that readers can master this material on their own without reasonable prior exposure to linear models and to issues in experimental design at the level of, say, *Statistical Methods*, the classic text of Snedecor and Cochran:

Another issue is software: this text is centered around SAS, and in fact the author notes that he has worked for years with Oliver Schabenberger, the developer of SAS’s POC GLIMMIX, and says that “we have been colleagues in thinking about what [the] GLMM curriculum should look like for years. The thought processes embedded in GLIMMIX reflect the way we think about GLMMs.” Hence 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: see http://www.sas.com/govedu/edu/programs/od_academics.html.

But as Stroup himself admits, “the statistics world seems to be moving toward R.” 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 is Professor of Mathematics at Georgetown College, in Kentucky. A typical Jack-of-All-Trades Small-College Mathematician, he enjoys the teaching of statistics at all levels, statistical consultation, and even institutional research. His interests and occasional forays into research in the history of mathematics include the geometrical works of Leonhard Euler and the mathematics of classical India.

**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**

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