Generalized Linear Mixed Models Modern Concepts, Methods and Applications

ISBN-10: 1439815127
ISBN-13: 9781439815120
Edition: 2012
Authors: Walter W. Stroup
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Description: This text covers statistical modeling using generalized linear mixed models (GLMMs) as the organizing tool. After an overarching introduction to modeling from a contemporary perspective, the book presents the main theory and methods used for setting  More...

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Book details

Copyright year: 2012
Publisher: CRC Press LLC
Publication date: 9/24/2012
Binding: Hardcover
Pages: 555
Size: 7.25" wide x 10.50" long x 1.25" tall
Weight: 2.442
Language: English

This text covers statistical modeling using generalized linear mixed models (GLMMs) as the organizing tool. After an overarching introduction to modeling from a contemporary perspective, the book presents the main theory and methods used for setting up estimation and inference for GLMMs. It also describes the major classes of applications with case studies from biostatistics and epidemiology. SAS is included throughout while R is used when SAS does not work well with the GLMM.

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
Estimation and Inference Essentials
Estimation
Introduction
Essential Background
Fixed Effects Only
Gaussian Mixed Models
Generalized Linear Mixed Models
Summary
Inference
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
Covariance Components
Introduction
Formal Testing of Covariance Components
Fit Statistics to Compare Covariance Models
Interval Estimation
Summary
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
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
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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