# Flexible Bayesian Quantile Regression in Ordinal Models 

Mohammad Arshad Rahman ∗ 

Department of Economic Sciences, Indian Institute of Technology Kanpur, India. Office: Faculty Building 672, IITK, Kanpur. Phone: +91 512-259-7010. Fax: +91 512-259-7570. 

## Abstract 

Risk Analyst, Model Risk Management, Credit Suisse, India 

Shubham Karnawat 

The paper introduces an estimation method for flexible Bayesian quantile regression in ordi- nal (FBQROR) models i.e., an ordinal quantile regression where the error follows a general- ized asymmetric Laplace (GAL) distribution. The GAL distribution, unlike the asymmetric Laplace (AL) distribution, allows to fix specific quantiles while simultaneously letting the mode, skewness and tails to vary. We also introduce the cumulative distribution function (necessary for constructing the likelihood) and the moment generating function of the GAL distribution. The algorithm is illustrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States. 

Keywords: Generalized asymmetric Laplace distribution, Gibbs sampling, Great 

Recession, homeownership, Markov chain Monte Carlo (MCMC), Metropolis-Hastings. 

## 1. Introduction 

Quantile regression, proposed by Koenker and Bassett (1978), models the conditional quantiles of the dependent variable as a function of the covariates. Since its introduc- 

