Abstract:

The problem of overdispersed claim counts and mismeasured covariates is common in insurance. On the one hand, the presence of overdispersion in the count data violates the homogeneity assumption, and on the other hand, measurement errors in covariates highlight the model risk issue in actuarial practice. In order to address these two problems simultaneously, we extend previous work on count-based generalized linear mixed models (GLMMs) by investigating a hierarchical Bayes framework coupled with some error-correction tools such as Simulation Extrapolation (SIMEX). Our goal is to demonstrate how this Bayesian GLMM approach captures unexplained correlations between observations that are associated with overdispersion and measurement error in actuarial practice. The improvements in inference are evaluated on the workplace absenteeism data.