Pseudo-R2D2 prior for high-dimensional ordinal regression

TL;DR

This paper introduces a novel Bayesian prior for high-dimensional ordinal regression that adapts the R2D2 framework using McFadden's R^2, enabling effective inference and prediction in gene expression studies.

Contribution

It extends the R2D2 prior to ordinal data by linking a generalized inverse Gaussian prior to McFadden's R^2, with implementation in Stan and R.

Findings

Demonstrates strong inference properties on simulated data.

Achieves accurate predictions on gene expression dataset.

Provides an accessible R package for implementation.

Abstract

Ordinal regression with a high-dimensional covariate space has many important application areas including gene expression studies. The lack of an intrinsic numeric value associated with ordinal responses, however, makes methods based on continuous data, like linear regression, inappropriate. In this work, we extend the R2D2 prior framework to the high-dimensional ordinal setting. Since the $R^2$ definition used in the R2D2 prior relies on means and variances, it cannot be used for ordinal regression as these two quantities are not suitable for such data. Instead, by simulating data and using McFadden's coefficient-of-determination ($R^2_M$), we show that a generalized inverse Gaussian prior distribution on the global variance parameter approximately induces a beta prior distribution on $R^2_M$. The proposed prior can be implemented in $\texttt{Stan}$ and an $\texttt{R}$ package is also developed. Our method demonstrates excellent inference properties on simulated data, as well as yielding accurate predictions when applied to a liver tissue gene expression dataset.