FREQUENTIST AND BAYESIAN ZERO-INFLATED REGRESSION MODELS ON INSURANCE CLAIM FREQUENCY: A COMPARISON STUDY USING MALAYSIA’S MOTOR INSURANCE DATA

Abstract

A no-claim event is a common scenario in insurance and the abundance of no-claim events can be described adequately by zero-inflated models. The zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models from frequentist and Bayesian approaches are considered for fitting to Malaysia’s motor insurance data. The results from the fittings are compared using mean absolute deviation and mean squared prediction error. The data is categorized into three claim types and the factors considered for regression modelling are coverage type, vehicle age, vehicle cubic capacity and vehicle make. The results from the fittings showed that the ZIP model from both approaches provide better fit than the ZINB model. Also, both ZIP and ZINB models from the Bayesian approach provide better fitting than the frequentist models. Therefore, Bayesian ZIP is the best model in explaining motor insurance claim frequency in Malaysia for all three claim types. From the best regression models, vehicle age, coverage type and vehicle make are the most influential factors in determining the frequency of claim for each claim type. Vehicle age and coverage type have positive effect on the frequency of claim whereas the vehicle make has negative effect on the frequency of claim.