Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies

Abstract

In this article, we propose a multivariate Pascal mixture regression model as an alternative to understand the association between multivariate count response variables and their covariates. When compared to the copula approach, this proposed class of regression models is not only less complex but can account for more versatile dependence structures and still allow for an intuitive explanation. We examine some of the properties possessed by this class of regression models and show its connections to several other models. For fitting purposes, we use the expectation-maximization (EM) algorithm which we find to be more effective and efficient. A by-product of this algorithm is that it provides for more reliable estimated standard errors of the regression coefficients useful for inference. Four different simulation studies are conducted to examine the performance of the fitting algorithm and the versatility of the proposed model while its applicability is additionally demonstrated by fitting an automobile insurance claim count dataset. All results are satisfactory and show that the proposed model can be a promising candidate for multivariate count regression modeling.