A Multivariate Generalized Poisson Regression Model

Abstract

A multivariate generalized Poisson regression model based on the multivariate generalized Poisson distribution is defined and studied. The regression model can be used to describe a count data with any type of dispersion. The model allows for both positive and negative correlation between any pair of the response variables. The parameters of the regression model are estimated by using the maximum likelihood method. Some test statistics are discussed, and two numerical data sets are used to illustrate the applications of the multivariate count data regression model.

Keywords:

• Correlated data
• Count data
• Estimation
• Over- and under-dispersion
• Test

Mathematics Subject Classification:

• Primary: 62F03, 62F10, 62H20
• Secondary: 62H12, 62J02, 62P10

Acknowledgment

The author is grateful for the comments and suggestions by the referees. Their comments and suggestions have greatly improved the article.