Random Effects in Generalized Linear Models

The levels used in a study for random effects represent a random sample from a much larger population of possible levels. Many studies involve mixed effects models where some regressors are fixed effects and some are random effects. Mixed effects models are useful for a wide array of study types. This chapter discusses the extension of linear regression models to linear mixed effect models and generalized linear models (GLMs) to generalized linear mixed models (GLMMs). It outlines a Bayesian approach to generalized linear mixed models. Some of the advantages afforded by this approach are emphasized. The chapter considers a Bayesian approach to modeling exponential family data with random effects. While the GLMM, hierarchical generalized linear models (HGLMs), and GEE approaches tend to focus primarily on inference for the population mean, the Bayesian approach offers a great deal of flexibility in terms of the types of distribution characteristics. Controlled Vocabulary Terms Bayesian inference; generalized linear mixed model