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 original 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 Stan and an \(\texttt {R}\) package is also developed. Our method demonstrates excellent coefficient estimation and variable selection properties on simulated data, and yields accurate predictions when applied to a liver tissue gene expression dataset.
