Score tests for overdispersion in poisson regression models

Abstract

Tests for detecting overdispersion in Poisson regression models are considered. A unified score test and a unified quasi-score test which can be applied to all compound Poisson alternatives are proposed for the linear or the quadratic variance-mean relation in modeling structures. The quasi-score test is identical to the score test for the quadratic relation. For the linear relation, the quasi-score test is as powerful as the score test. However computing its significance level can be made even more accurate by using distributional approximations. Simulations are conducted for power comparison among the present tests for three different compound Poisson distributions.