Two-component Poisson mixture regression modelling of count data with bivariate random effects

Two-component Poisson mixture regression is typically used to model heterogeneous count outcomes that arise from two underlying sub-populations. Furthermore, a random component can be incorporated into the linear predictor to account for the clustering data structure. However, when including random effects in both components of the mixture model, the two random effects are often assumed to be independent for simplicity. A two-component Poisson mixture regression model with bivariate random effects is proposed to deal with the correlated situation. A restricted maximum quasi-likelihood estimation procedure is provided to obtain the parameter estimates of the model. A simulation study shows both fixed effects and variance component estimates perform well under different conditions. An application to childhood gastroenteritis data demonstrates the usefulness of the proposed methodology, and suggests that neglecting the inherent correlation between random effects may lead to incorrect inferences concerning the count outcomes.