Multiple inflated negative binomial regression for correlated multivariate count data

This article aims to provide a method of regression for multivariate multiple inflated count responses assuming the responses follow a negative binomial distribution. Negative binomial regression models are common in the literature for modeling univariate and multivariate count data. However, two problems commonly arise in modeling such data: choice of the multivariate form of the underlying distribution and modeling the zero-inflated structure of the data. Copula functions have become a popular solution to the former problem because they can model the response variables' dependence structure. The latter problem is often solved by modeling an assumed latent variable Z generating excess zero-valued counts in addition to the underlying distribution. However, despite their flexibility, zero-inflation models do not account for the case of m additional inflated values at k(1), k(2), ..., k(m). We propose a multivariate multiple-inflated negative binomial regression model for modeling such cases. Furthermore, we present an iterative procedure for estimating model parameters using maximum likelihood estimation. The multivariate distribution functions considering the dependence structure of the response vectors are found using copula methods. The proposed method is illustrated using simulated data and applied to real data.