Generalized linear models with clustered data: Fixed and random effects models

The statistical analysis of mixed effects models for binary and count data is investigated. In the statistical computing environment R, there are a few packages that estimate models of this kind. The package lme4 is a de facto standard for mixed effects models. The package glmmML allows non-normal distributions in the specification of random intercepts. It also allows for the estimation of a fixed effects model, assuming that all cluster intercepts are distinct fixed parameters; moreover, a bootstrapping technique is implemented to replace asymptotic analysis. The random intercepts model is fitted using a maximum likelihood estimator with adaptive Gauss–Hermite and Laplace quadrature approximations of the likelihood function. The fixed effects model is fitted through a profiling approach, which is necessary when the number of clusters is large. In a simulation study, the two approaches are compared. The fixed effects model has severe bias when the mixed effects variance is positive and the number of clusters is large.

► Generalized linear models with clustering are studied with the RR package eha.
► Fixed and random effects approaches are compared.
► For random effects models, we introduce other mixing distributions than the normal.
► For fixed effects models, profiling is introduced.
► For data with many clusters, the fixed effects modelling is inferior.