Likelihood-based analysis of longitudinal count data using a generalized Poisson model

Models based on a generalization of the simple Poisson process are discussed and illustrated with an analysis of some longitudinal count data on frequencies of epileptic fits. The models enable a broad class of discrete distributions to be constructed, which cover a variety of dispersion properties that can be characterized in an intuitive and appealing way by a simple parameterization. This class includes the Poisson and negative binomial distributions as well as other distributions with greater dispersion than Poisson, and also distributions underdispersed relative to the Poisson distribution. Comparing a number of analyses of the data shows that some covariates have a more significant effect using this modelling than from using mixed Poisson models. It is argued that this could be due to the mixed Poisson models used in the other analyses not providing an appropriate description of the residual variation, with the greater flexibility of the generalized Poisson modelling generally enabling more critical assessment of covariate effects than more standard mixed Poisson modelling.