1st Edition

Multivariate Generalized Linear Mixed Models Using R

    304 Pages 18 B/W Illustrations
    by CRC Press

    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.


    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.


    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.
    —Sebnem Er, Journal of Applied Statistics, 2012