Modelling multivariate, overdispersed count data with correlated and non-normal heterogeneity effects

Mixed Poisson models are most relevant to the analysis of longitudinal count data in various disciplines. A conventional specification of such models relies on the normality of unobserved heterogeneity effects. In practice, such an assumption may be invalid, and non-normal cases are appealing. In this paper, we propose a modelling strategy by allowing the vector of effects to follow the multivariate skew-normal distribution. It can produce dependence between the correlated longitudinal counts by imposing several structures of mixing priors. In a Bayesian setting, the estimation process proceeds by sampling variants from the posterior distributions. We highlight the usefulness of our approach by conducting a simulation study and analysing two real-life data sets taken from the German Socioeconomic Panel and the US Centers for Disease Control and Prevention. By a comparative study, we indicate that the new approach can produce more reliable results compared to traditional mixed models to fit correlated count data