Flexible Bayesian Quantile Regression in Ordinal Models

TL;DR

This paper develops a flexible Bayesian quantile regression method for ordinal models using a generalized asymmetric Laplace distribution, allowing for more adaptable modeling of skewness and tails.

Contribution

It introduces the GAL distribution for ordinal quantile regression, providing a more flexible approach than existing models, along with the necessary distribution functions.

Findings

Effective in simulation studies

Applied to US public opinion data

Demonstrates modeling flexibility

Abstract

The paper introduces an estimation method for flexible Bayesian quantile regression in ordinal (FBQROR) models i.e., an ordinal quantile regression where the error follows a generalized 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.