Modeling the Amount of Insurance Claim using Gamma Linear Mixed Model with AR (1) random effect

The amount of insurance claims is continuous data and is positive so it is usually assumed to have gamma distribution. Usually, Generalized Linear Model (GLM)'s approach is used since the gamma distribution is a member of the exponential family. In case there is a random effect in modeling, then GLM can be extended to Generalized Linear Mixed Model (GLMM). This study models the amount of insurance claims with the most GLMM's approach using two random effects, namely the region and time of the occurrence which is assumed to follow a first-order autoregressive process. The h-likelihood method is used to estimate the regression parameters and the variance parameters. A simulation study is carried out with an evaluation using the average relative bias and the average MSE. An application study which is conducted to model the amount of insurance claims in a certain region and time based on the 2014 profile of risk and loss of motor vehicle insurance in Indonesia is also carried out.