Score Test for Testing Poisson Regression against Generalized Poisson Alternatives

摘要

Poisson regression model has been considered as a standard method for modeling count data. However, count data often display overdispersion, and thus, negative binomial (NB) regression model has been suggested for handling overdispersed count data. In addition, generalized Poisson (GP) regression model has been proposed for handling both over- and underdispersed count data. This study proposes the score test for testing Poisson regression against GP alternatives and proves that it is equal to the score test for testing Poisson regression against NB alternatives. The advantage of score test over other alternative tests such as likelihood ratio and Wald is that the score test can be used to determine whether a more complex model is appropriate without fitting the more complex model. Application of the proposed score test on the Malaysian private car claim count data is illustrated.