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.

翻译：保险业中过度离散索赔计数与测量误差协变量问题普遍存在。一方面，计数数据中的过度离散性违反了同质性假设；另一方面，协变量的测量误差凸显了精算实务中的模型风险问题。上述问题可能导致保费定价不精准，进而影响业务竞争力。本研究的目标是通过捕捉精算过程中因过度离散结果与测量误差协变量产生的不可观测观测间相关性，同时解决这两个建模难题。为此，我们在基于计数的广义线性混合模型（GLMM）与非线性建模中常用的误差校正工具——模拟外推法（SIMEX）之间建立了创新性关联。我们提出基于分层贝叶斯范式的建模框架。据我们所知，将分层贝叶斯与SIMEX相结合的方法此前尚未在文献中探讨过。我们通过工作缺勤数据验证了该方法的适用性。结果表明：融合SIMEX的分层贝叶斯GLMM在拟合优度方面优于朴素GLMM/SIMEX模型。