Testing for Homogeneity of Dispersion Parameters under Overdispersion in Nonlinear Poisson-Gamma Regression Models

Poisson regression models are widely used in analyzing count data. However, overdispersion often exists in these models. Two ways of modelling overdispersion in Poisson regression models are quasi-likelihood approach and random-effect approach. Many authors have discussed the tests for detecting overdispersion in Poisson models using random-effect methods. But they all assumed that the random effects were mutually independent and identically ditributed. This paper presents the test for their assumptions. We develop two diagnostic tests for homogeneity of dispersion parameters in over-dispersion nonlinear random-effect Poisson-Gamma models conditionally on identical and diffrent within-subject effects respectively. The score test statistics are obtained and two numerical examples are given to illustrate our results.