Gaussian copula-based zero-inflated power series joint models to analyze correlated count data

Abstract

A Gaussian Copula-based regression model is proposed that accounts for associations between count responses with extra zeros. Our approach entails underlying latent variables to indicate the latent mechanisms which generate the count responses where some of the count responses are inflated in a zero point. The model contains, as special sub-models, several important distributions such as the power series distributions with and without extra zeros, for example, Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions. The full likelihood-based inference method is applied for the estimation of parameters to obtain maximum likelihood estimates of the parameters. Modified Pearson residuals, where the correlation between responses is taken into account, are used for finding abnormal observations. To illustrate the utility of the models, some simulations are illustrated. Finally, the proposed models are applied to an insurance data set for insurers, obtained from an observational study, where the number of automobile claims and the number of third party claims are the correlated count responses. The effects of car age and the type of car, driving place on both responses are investigated simultaneously.