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 assumptionmay 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.
Modelling multivariate, overdispersed count data with correlated and non-normal heterogeneity effects
Descripción:
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 assumptionmay 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.