Score tests for bivariate zero-inflated negative binomial regression model

This study proposes score tests for testing zero-inflation, the dependency parameter, independence, and overdispersion in the generalized bivariate zero-inflated negative binomial (GBZINB) regression model based on the Sarmanov family. In particular, we proposed a one-sided joint score test for testing overdispersion because the BZINB model has two dispersion parameters that are always positive. This leads to a one-sided score test for multi-parameters which has rarely been addressed in bivariate count data regression models. In addition, we used a Monte Carlo study to verify the efficiency of the proposed score tests in this study and their corresponding likelihood ratio (LR) tests. From the Monte Carlo study, we found that the score and LR tests for testing zero-inflation, for testing the dependency parameter, and for testing independence maintained the nominal significance level and showed similar estimated power. However, both tests underestimate the nominal significance level when testing for overdispersion. The degree of underestimation of the nominal significance level of the score test was more severe than that in the LR test. An empirical example from data of 1977-1978 Australian Health Survey was provided to illustrate the results of the proposed tests.