Bayesian Quantile Regression for Ordinal Models

TL;DR

This paper develops Bayesian methods for quantile regression in ordinal models, providing algorithms that improve estimation accuracy and utility in economic and political science applications.

Contribution

It introduces novel Bayesian algorithms for quantile regression in ordinal models using latent variable frameworks and MCMC techniques.

Findings

Algorithms perform well in simulation studies

Effective in analyzing educational attainment data

Useful for modeling public opinion on policy issues

Abstract

The paper introduces a Bayesian estimation method for quantile regression in univariate ordinal models. Two algorithms are presented that utilize the latent variable inferential framework of Albert and Chib (1993) and the normal-exponential mixture representation of the asymmetric Laplace distribution. Estimation utilizes Markov chain Monte Carlo simulation - either Gibbs sampling together with the Metropolis-Hastings algorithm or only Gibbs sampling. The algorithms are employed in two simulation studies and implemented in the analysis of problems in economics (educational attainment) and political economy (public opinion on extending "Bush Tax" cuts). Investigations into model comparison exemplify the practical utility of quantile ordinal models.