Bayesian Ordinal Quantile Regression with a Partially Collapsed Gibbs Sampler

TL;DR

This paper introduces BORPS, a Bayesian ordinal quantile regression method with a partially collapsed Gibbs sampler, addressing the lack of effective techniques for ordinal data and demonstrating superior performance on simulations and real data.

Contribution

The paper proposes a novel Bayesian ordinal quantile regression approach with a partially collapsed Gibbs sampler, improving analysis of ordinal data over existing methods.

Findings

BORPS outperforms existing methods in simulations.

Application to real data reveals new insights into early puberty.

Software implementation is publicly available.

Abstract

Unlike standard linear regression, quantile regression captures the relationship between covariates and the conditional response distribution as a whole, rather than only the relationship between covariates and the expected value of the conditional response. However, while there are well-established quantile regression methods for continuous variables and some forms of discrete data, there is no widely accepted method for ordinal variables, despite their importance in many medical contexts. In this work, we describe two existing ordinal quantile regression methods and demonstrate their weaknesses. We then propose a new method, Bayesian ordinal quantile regression with a partially collapsed Gibbs sampler (BORPS). We show superior results using BORPS versus existing methods on an extensive set of simulations. We further illustrate the benefits of our method by applying BORPS to the Fragile Families and Child Wellbeing Study data to tease apart associations with early puberty among both genders. Software is available at: GitHub.com/igrabski/borps.