Tests for independence in a bivariate negative binomial model

The score test and LR test statistic for testing independence are proposed in a bivariate negative binomial regression model. We also propose an adjusted score test in order to enhance the efficiency of the score test. This study is an extension of the work in a univariate model by Dean and Lawless [Dean, C., Lawless, F. (1989). Tests for detecting overdispersion in Poisson regression models. Journal of the American Statistical Association, 84, 467–472]. The adjusted score test proposed in this study is more efficient than the complicated LR test.