A Bayesian two-part quantile regression model for count data with excess zeros

Abstract

Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables produced by a single data-generating process. Of the few studies that have performed QR on count data, none have accounted for excess zeros from a Bayesian perspective, as does the hurdle model that we propose. In this article, we propose a Bayesian two-part QR model for count data with excess zeros. The proposed model is compared to a frequentist approach via simulation, and its usefulness is displayed on two real datasets. In each application, multiple covariates are found to have differing effects across the response distribution, with special attention given to the nature of those effects in the outermost response distribution quantiles.