  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. The consequence can be inaccurate premium pricing which would
negatively affect business competitiveness. Our goal is to address these two
modelling problems simultaneously by capturing the unobservable correlations
between observations that arise from overdispersed outcome and mismeasured
covariate in actuarial process. To this end, we establish novel connections
between the count-based generalized linear mixed model (GLMM) and a popular
error-correction tool for non-linear modelling - Simulation Extrapolation
(SIMEX). We consider a modelling framework based on the hierarchical Bayesian
paradigm. To our knowledge, the approach of combining a hierarchical Bayes with
SIMEX has not previously been discussed in the literature. We demonstrate the
applicability of our approach on the workplace absenteeism data. Our results
indicate that the hierarchical Bayesian GLMM incorporated with the SIMEX
outperforms naive GLMM / SIMEX in terms of goodness of fit.
