Bayesian Estimation for Zero-Truncated Bivariate Poisson Regression Model

Abstract

Bivariate count data occurs when two associated variable counts necessitate joint estimate primarily for efficiency purposes. This paper presents Bayesian estimate for the zero-truncated bivariate Poisson regression model. This bivariate model was established using marginal-conditional models. Bayes estimators were executed utilizing the random walk Metropolis-Hastings algorithm with two distinct prior distributions: Laplace and normal distributions. Moreover, estimators employing the bootstrap approach were proposed. Additionally, the credible intervals and the percentile bootstrap confidence intervals were analyzed. The performance of the Bayes estimators was compared with that of the bootstrap estimators and the maximum likelihood estimators via a Monte Carlo simulation analysis, focusing on mean square error. The performance of intervals was evaluated based on coverage probability and average length. Furthermore, the explanatory variables were produced under conditions of both multicollinearity and a lack of multicollinearity. Two empirical datasets were examined to demonstrate the practical use of the suggested model and methodology. The findings from both the simulation and application indicate that the Bayesian method with a normal prior distribution surpasses alternative methods.