On a Mixed Poisson Liu Regression Estimator for Overdispersed and Multicollinear Count Data

Abstract

e Poisson regression model is a commonly used statistical method for analyzing the count response variable [1]. One disadvantage of this model is that it is an overdispersion issue that is common in the real-world applications of actuarial, engineering, biomedical, and economic sciences. e overdispersion occurs when the conditional variance of the count response variable exceeds the conditional mean of the count response variable. In this context, the index of dispersion (variance-to-mean ratio) is greater than one. To tackle this issue in the Poisson regression model, researchers have proposed several mixed Poisson regression models. e standard mixed Poisson distribution is obviously the negative binomial (NB)/Poisson-gamma regression model introduced by Greenwood and Yule [2]. However, the NB distribution fails to t well for a count data with a higher value of the index of dispersion and long right-tail behavior. en, the regression model based on NB is not a good choice for such a count response variable. As an alternative to the NB regression model, several mixed Poisson regression models are in the literature. However, most of the probability mass functions (pmfs) of these mixed Poisson distributions are not in an explicit form. Some notable examples of such regression models are the Poisson-Inverse Gaussian regression model [3] and the Poisson-Inverse gamma regression model [4]. is algebraic intractability in such distributions leads to computational complexity, and their regression models are limited in practice.