Inference sensitivity for Poisson mixtures

Abstract

Data presented as contingency tables and classified by qualitative or quantitative methods are usually analysed on the basis of a Poisson log linear model. We examine the effect of Poisson mixtures, especially as represented by the negative binomial distribution, on statistical inference. The main finding is that probabilities of rejection are increased, sometimes considerably. In the case of heterogeneous binary data, attention is also given to the problems of analysis implied by Poisson mixtures.