GEE-based Bell model for longitudinal count outcomes

Longitudinal count models are usually constructed based on Poisson and negative binomial distributions. Recently, a single-parameter discrete Bell distribution has been presented as an alternative to well-known count distributions. In this study, a new marginal model is proposed for longitudinal count responses based on Bell distribution to handle overdispersion and dependency structure. Bell distribution is more practical in that it has fewer parameters than the negative binomial distribution and still handle overdispersion with a single parameter. Focusing on demonstrating that regression diagnostics supplement the Bell marginal model based on GEE to serve as sensitivity analysis. The Bell marginal model is used to analyze the number of accidents caused injuries in Greece during the 5-year time period. The half-normality plots indicate that the Bell marginal model provides better fit than other marginal models for the accident dataset. The common working covariance selection criterias and properties of parameter estimations are investigated for the Bell marginal model in the simulation study. Parameter estimations of the new model based on GEEs are obtained by geeM R package with the user-defined function. Diagnostic measures and simulated envelope algorithm are also provided for the proposed model.