DESIGNING AN OFFSET POISSON-GAMMA MIXTURE REGRESSION MODEL

Abstract

The problem of over-dispersion often encountered by Poisson distribution is what gave rise to the development of the Poisson-Gamma mixture distribution. This distribution is a mixture of a family of Poisson distributions with Gamma mixing weights. The log likelihood function of the Poisson-Gamma mixture distribution has been exponentiated in order to extract the canonical link of the mixture distribution. This link function is re-expressed as a sum of the loglinear link and an offset. By implication, modeling for the Poisson-Gamma mixture model amounts to modeling for the Poisson loglinear model and adding the offset term to the result. This model can be used to model HIV/AIDS infection rate for multiple sex partners. It is theoretically shown that the mixture distribution reduces to the Poisson distribution and that in large samples, the Poisson-Gamma mixture is approximated by the Poisson distribution.