Comparison of Additive and Multiplicative Bayesian Models for Longitudinal Count Data with Overdispersion Parameters: A Simulation Study

In applied statistical data analysis, overdispersion is a common feature. It can be addressed using both multiplicative and additive random effects. A multiplicative model for count data incorporates a gamma random effect as a multiplicative factor into the mean, whereas an additive model assumes a normally distributed random effect, entered into the linear predictor. Using Bayesian principles, these ideas are applied to longitudinal count data, based on the so-called combined model. The performance of the additive and multiplicative approaches is compared using a simulation study.