Generalized Linear Mixed Effects Models

This chapter describes how generalized linear models can be extended to longitudinal data. These models are known as generalized linear mixed effects models (GLMMs). The chapter examines first the linear mixed effects model as a generalized linear model, albeit one with both fixed and random effects, and then looks at how the ideas underlying the linear mixed effects model can be extended to generalized linear models. The introduction of random effects has important implications for the interpretation of the regression coefficients in GLMMs. Although the inclusion of random coefficients induces overdispersion marginally, the model nonetheless assumes Poisson variation conditional on these subject-specific effects and the covariates. The chapter briefly describes maximum likelihood estimation of the fixed effects and the random effects covariance parameters. It also illustrates GLMMs for analyzing longitudinal data from three case studies. The chapter ends with a discussion on fitting GLMMs using standard statistical software.