Generalized linear mixed-effects models

Abstract

Generalized linear mixed-effects models, more commonly known as generalized linear mixed models, are very popular in longitudinal data analysis. They are a natural combination of two modeling strands, linear mixed models and generalized linear models. Linear mixed models (e.g., Harville, 1977; Laird and Ware, 1982) are linear regression models that include normally distributed random effects in addition to fixed effects. A natural application is to longitudinal data where the random effects vary between subjects and induce within-subject dependence among repeated measurements after conditioning on observed covariates. Generalized linear models (Nelder and Wedderburn, 1972; Wedderburn, 1974)unify regression models for different response types such as linear models for continuous responses, logistic models for binary responses, and log-linear models for counts.