Fitting the bivariate mixed Poisson regression model by maximum simulated likelihood

We introduce bimpoisson, a program to fit the bivariate mixed Poisson regression model by maximum simulated likelihood using the two approaches proposed by Munkin and Trivedi ("Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application", The Econometrics Journal 2, 1999, 29-48). By default, bimpoisson uses their sampling function approach; optionally their standard MSL approach is available. bimpoisson allows either pseudo-random uniform draws or Halton draws for simulation. Additional options allow use of antithetic acceleration and a first-order bias correction. Like Jumamyradov and Munkin ("Biases in maximum simulated likelihood estimation of bivariate models", Journal of Econometric Methods 11, 2022, 55-70), we use a modified version of Munkin and Trivedi's sampling function to provide better coverage. We also provide post-estimation tools to predict conditional count probabilities and expected counts. We examine bimpoisson's performance using Monte Carlo simulation analysis and our empirical illustrations fit models using the same bivariate count data as used by Xu and Hardin ("Regression models for bivariate count outcomes", The Stata Journal, 16, 2016, 301-315) and Munkin and Trivedi (1999). We provide practical advice about which MSL estimator and types of draws and number to use.