Statistical Inference For A Bivariate Poisson Regression Model

Bivariate Poisson regression models allow for joint estimation of two Poisson counts as a function of possibly different covariates. We use vector calculus to derive the Wald, score, and likelihood ratio statistics for testing a single coefficient parameter vector. We compare the power of these three statistics using a limited Monte Carlo simulation study. We also develop a Wald statistic for testing the equality of two regression coefficient vectors. Lastly, we apply the newly-derived test statistics to an Australian health survey data set.