Comparisons of some bivariate regression models

Abstract

The bivariate negative binomial regression (BNBR) and the bivariate Poisson log-normal regression (BPLR) models have been used to describe count data that are over-dispersed. In this paper, a new bivariate generalized Poisson regression (BGPR) model is defined. An advantage of the new regression model over the BNBR and BPLR models is that the BGPR can be used to model bivariate count data with either over-dispersion or under-dispersion. In this paper, we carry out a simulation study to compare the three regression models when the true data-generating process exhibits over-dispersion. In the simulation experiment, we observe that the bivariate generalized Poisson regression model performs better than the bivariate negative binomial regression model and the BPLR model.

Keywords:

• non-nested models
• Monte Carlo simulation
• likelihood ratio test
• over-dispersion

Acknowledgements

This work was done while Felix Famoye, Central Michigan University,was on sabbatical leave at the Department of Mathematics, University of Lagos, Nigeria. The author gratefully acknowledges the support received from the US Department of State, Bureau of Education and Cultural Affairs under the grant #09-78737. The author is grateful to the anonymous reviewers for their valuable suggestions that improved the presentation.