Generalized Poisson Regression: An Alternative for Risk Classification

The Poisson regression model has been widely used for risk classification in the recent years. However, the Poisson regression model assumes that the mean and variance of the dependent variable is equal, whereas in practice, the data may display overdispersion or extra- Poisson variation, i.e., a situation where the variance exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standard errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. Therefore, the objective of this paper is to suggest the Generalized Poisson regression model as an alternative for risk classification. In this paper, the Poisson and Generalized Poisson regression models are fitted, tested and compared on two types of Malaysian motor insurance claims count data; Own Damage (OD) and Third Party Bodily Injury (TPBI). The Poisson regression model for OD claims gives large values for Pearson chi-squares and deviance, indicating possible existence of overdispersion. Based on the results of goodness-of-fit tests, the Generalized Poisson is superior to the Poisson. On the contrary, the small deviance for Poisson regression model in TPBI claims implies that the model is adequate. Based on the likelihood ratio test, the likelihood ratio is insignificant, implying that the Poisson is adequate.