Comparison of Bivariate Negative Binomial Regression Models for Handling Over Dispersion.

Abstract

Some methods have been proposed for dealing with extra Poisson variation when conducting regression analysis of count data. One of them is negative binomial regression model. For bivariate cases, there are some methods for constructing bivariate negative binomial distributions. Two of them are bivariate negative binomial distribution as a mixture Poisson gamma and a result of multiplication of negative binomial marginals by a multiplicative factor. In this paper we will review the bivariate negative binomial regression models based on those distributions by using maximum likelihood estimation (MLE) method, including the parameters estimation and hypothesis testing. We use health care datasets as the application. The bivariate negative binomial models tend to give better performance than the bivariate Poisson models for analyzing the data with over-dispersion. In this work, a model that comes from a result of multiplication of negative binomial marginals by a multiplicative factor has best performance in modeling the health care data.