Mixed Poisson regression models with covariate dependent rates

This paper studies a class of Poisson mixture models that includes covariates in rates. This model contains Poisson regression and independent Poisson mixtures as special cases. Estimation methods based on the EM and quasi-Newton algorithms, properties of these estimates, a model selection procedure, residual analysis, and goodness-of-fit test are discussed. A Monte Carlo study investigates implementation and model choice issues. This methodology is used to analyze seizure frequency and Ames salmonella assay data.