bqror: An R package for Bayesian Quantile Regression in Ordinal Models

Abstract

This article describes an R package bqror that estimates Bayesian quantile regression for ordinal models introduced in \citet{Rahman-2016}. The paper classifies ordinal models into two types and offers two computationally efficient, yet simple, MCMC algorithms for estimating ordinal quantile regression. The generic ordinal model with more than 3 outcomes (labeled $OR_{I}$ model) is estimated by a combination of Gibbs sampling and Metropolis-Hastings algorithm. Whereas an ordinal model with exactly 3 outcomes (labeled $OR_{II}$ model) is estimated using Gibbs sampling only. In line with the Bayesian literature, we suggest using marginal likelihood for comparing alternative quantile regression models and explain how to calculate the same. The models and their estimation procedures are illustrated via multiple simulation studies and implemented in the two applications presented in \citet{Rahman-2016}. The article also describes several other functions contained within the bqror package, which are necessary for estimation, inference, and assessing model fit.