A Random-Effects Log-Linear Model with Poisson Distributions

Abstract

In several applications data are grouped and there are within-group correlations. With continuous data, there are several available models that are often used; with counting data, the Poisson distribution is the natural choice. In this paper a mixed log-linear model based on a Poisson–Poisson conditional distribution is presented. The initial model is a conditional model for the mean of the response variable, and the marginal model is formed thereafter. Random effects with Poisson distribution are introduced and a variance-covariance matrix for the response vector is formed embodying the covariance structure induced by the grouping of the data.