1st Edition

# Multivariate Generalized Linear Mixed Models Using R

304 Pages 18 B/W Illustrations
by CRC Press

304 Pages
by CRC Press

Also available as eBook on:

Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.

A Unified Framework for a Broad Class of Models
The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model estimation, and endogenous variables, along with SabreR commands and examples.

Improve Your Longitudinal Study
In medical and social science research, MGLMMs help disentangle state dependence from incidental parameters. Focusing on these sophisticated data analysis techniques, this book explains the statistical theory and modeling involved in longitudinal studies. Many examples throughout the text illustrate the analysis of real-world data sets. Exercises, solutions, and other material are available on a supporting website.

Introduction

Generalized Linear Models for Continuous/Interval Scale Data
Introduction
Continuous/interval scale data
Simple and multiple linear regression models
Checking assumptions in linear regression models
Likelihood: multiple linear regression
Comparing model likelihoods
Application of a multiple linear regression model

Generalized Linear Models for Other Types of Data
Binary data
Ordinal data
Count data

Family of Generalized Linear Models
Introduction
The linear model
Binary response models
Poisson model
Likelihood

Mixed Models for Continuous/Interval Scale Data
Introduction
Linear mixed model
The intraclass correlation coefficient
Parameter estimation by maximum likelihood
Regression with level-two effects
Two-level random intercept models
General two-level models including random intercepts
Likelihood
Residuals
Checking assumptions in mixed models
Comparing model likelihoods
Application of a two-level linear model
Two-level growth models
Likelihood
Example on linear growth models

Mixed Models for Binary Data
Introduction
The two-level logistic model
General two-level logistic models
Intraclass correlation coefficient
Likelihood
Example on binary data

Mixed Models for Ordinal Data
Introduction
The two-level ordered logit model
Likelihood
Example on mixed models for ordered data

Mixed Models for Count Data
Introduction
The two-level Poisson model
Likelihood
Example on mixed models for count data

Family of Two-Level Generalized Linear Models
Introduction
The mixed linear model
Mixed binary response models
Mixed Poisson model
Likelihood

Three-Level Generalized Linear Models
Introduction
Three-level random intercept models
Three-level generalized linear models
Linear models
Binary response models
Likelihood
Example on three-level generalized linear models

Models for Multivariate Data
Introduction
Multivariate two-level generalized linear model
Bivariate Poisson model: Example
Bivariate ordered response model: Example
Bivariate linear-probit model: Example
Multivariate two-level generalized linear model likelihood

Models for Duration and Event History Data
Introduction
Duration data in discrete time
Renewal data
Competing risk data

Stayers, Non-Susceptibles, and Endpoints
Introduction
Mover-stayer model
Likelihood with mover-stayer model
Example 1: Stayers in Poisson data
Example 2: Stayers in binary data

Handling Initial Conditions/State Dependence in Binary Data
Introduction to key issues: heterogeneity, state dependence and non-stationarity
Motivational example
Random effects model
Initial conditions problem
Initial treatment of initial conditions problem
Example: Depression data
Classical conditional analysis
Classical conditional model: Depression example
Conditioning on initial response but allowing random effect u0j to be dependent on zj
Wooldridge conditional model: Depression example
Modeling the initial conditions
Same random effect in the initial response and subsequent response models with a common scale parameter
Joint analysis with a common random effect: Depression example
Same random effect in models of the initial response and subsequent responses but with different scale parameters
Joint analysis with a common random effect (different scale parameters): Depression example
Different random effects in models of the initial response and subsequent responses
Different random effects: Depression example
Embedding the Wooldridge approach in joint models for the initial response and subsequent responses
Joint model plus the Wooldridge approach: Depression example

Incidental Parameters: An Empirical Comparison of Fixed Effects and Random Effects Models
Introduction
Fixed effects treatment of the two-level linear model
Dummy variable specification of the fixed effects model
Empirical comparison of two-level fixed effects and random effects estimators
Implicit fixed effects estimator
Random effects models
Comparing two-level fixed effects and random effects models
Fixed effects treatment of the three-level linear model

Appendix A: SabreR Installation, SabreR Commands, Quadrature, Estimation, Endogenous Effects
Appendix B: Introduction to R for Sabre

Bibliography

Exercises appear at the end of most chapters.

### Biography

Damon M. Berridge is a senior lecturer in the Department of Mathematics and Statistics at Lancaster University. Dr. Berridge has nearly 20 years of experience as a statistical consultant. His research focuses on the modeling of binary and ordinal recurrent events through random effects models, with application in medical and social statistics.

Robert Crouchley is a professor of applied statistics and director of the Centre for e-Science at Lancaster University. His research interests involve the development of statistical methods and software for causal inference in nonexperimental data. These methods include models for errors in variables, missing data, heterogeneity, state dependence, nonstationarity, event history data, and selection effects.

I think this is a very well organised and written book and therefore I highly recommend it not only to professionals and students but also to applied researchers from many research areas such as education, psychology and economics working on complex and large data sets.
â€”Sebnem Er, Journal of Applied Statistics, 2012