Multivariate Generalized Linear Mixed Models Using R

By Damon Mark Berridge, Robert Crouchley

© 2011 – CRC Press

304 pages | 18 B/W Illus.

Purchasing Options:
Hardback: 9781439813263
pub: 2011-04-24
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About the Book

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.


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.

—Sebnem Er, Journal of Applied Statistics, 2012

Table of Contents


Generalized Linear Models for Continuous/Interval Scale Data


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


The linear model

Binary response models

Poisson model


Mixed Models for Continuous/Interval Scale Data


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



Checking assumptions in mixed models

Comparing model likelihoods

Application of a two-level linear model

Two-level growth models


Example on linear growth models

Mixed Models for Binary Data


The two-level logistic model

General two-level logistic models

Intraclass correlation coefficient


Example on binary data

Mixed Models for Ordinal Data


The two-level ordered logit model


Example on mixed models for ordered data

Mixed Models for Count Data


The two-level Poisson model


Example on mixed models for count data

Family of Two-Level Generalized Linear Models


The mixed linear model

Mixed binary response models

Mixed Poisson model


Three-Level Generalized Linear Models


Three-level random intercept models

Three-level generalized linear models

Linear models

Binary response models


Example on three-level generalized linear models

Models for Multivariate Data


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


Duration data in discrete time

Renewal data

Competing risk data

Stayers, Non-Susceptibles, and Endpoints


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

Other link functions

Incidental Parameters: An Empirical Comparison of Fixed Effects and Random Effects Models


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


Exercises appear at the end of most chapters.

About the Authors

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.

Subject Categories

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