A RANDOM-EFFECTS LOG-LINEAR MODEL WITH POISSON DISTRIBUTIONS

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 e®ects 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. Key-Words: log-linear models; grouped data; random e®ects; mixed models; overdispersion; iterative reweighted generalized least squares. AMS Subject Classi¯cation