Generalized Linear Mixed Models: Modern Concepts, Methods and Applications
Features
- Provides a true introduction to linear modeling that assumes data need not be normally distributed and assumes random model effects to be the rule not an advanced exception
- Emphasizes the connection between study design and all aspects of the model
- Includes a chapter on GLMM-based power and sample size assessment—a critical tool for cost-effective design of research studies
- Presents numerous examples using the SAS GLIMMIX procedure
- Gives in-depth treatments of issues unique to generalized and mixed linear modeling, including conditional versus marginal modeling, broad versus narrow inference space, and data versus model-scale inference and reporting
- Offers the data for all exercises as well as SAS files for all examples at www.crcpress.com
Summary
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.
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
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
Editorial Reviews
"… 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
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| SASDataProgFiles.zip | Cross Platform | October 22, 2012 | SAS Data & Program Files |
