Generalized Linear Mixed Models for Predicting Non-Life Insurance Claims

Abstract

Generalized linear mixed models (or GLMMs) are an extension of linear mixed models to allow response variables from different distributions. Alternatively, GLMMs are an extension of generalized linear models (GLMs) to include both fixed and random effects (hence mixed models) that can be used as a modeling approach that allows the modeling of nonlinear behaviors and non-Gaussian distributions of residues. These models are very useful for general insurance claim predictions, where the frequency and the severity of claims distributions are usually non-Gaussian. In our research, we shall compare the performance of GLMS and that of GLMMS to estimate the aggregate of claims of auto insurance. The data used are a secondary dataset which is the motor vehicle dataset from Australia named ausprivauto0405. The results of our research suggest that GLMMs approach does not always give the best estimations and even in some cases GLMs outperform GLMMs. The accuracy of the models was compared to choosing the best model for determining pure insurance premiums using R software. More investigation using different models is needed to ensure which model is more appropriate for estimating the aggregate of insurance claims.