Bayesian non-parametric ordinal regression under a monotonicity constraint

TL;DR

This paper introduces a Bayesian non-parametric ordinal regression model that enforces monotonicity constraints on covariate effects, allowing flexible shape approximation and covariate selection, suitable for ordinal outcome data.

Contribution

It generalizes previous Bayesian monotonic regression models to ordinal outcomes using a marked point process approach with reversible jump MCMC, offering a flexible and interpretable inference framework.

Findings

The model accurately captures monotonic relationships in simulated data.

It effectively performs covariate selection in regression tasks.

Applied to real datasets, it demonstrates practical utility and interpretability.

Abstract

Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds model, but there it is combined with other parametric assumptions such as linearity and additivity. Herein, the considered models are non-parametric and the only condition imposed is that the effects of the covariates on the outcome categories are stochastically monotone according to the ordinal scale. We are not aware of the existence of other comparable multivariable models that would be suitable for inference purposes. We generalize our previously proposed Bayesian monotonic multivariable regression model to ordinal outcomes, and propose an estimation procedure based on reversible jump Markov chain Monte Carlo. The model is based on a marked point process construction, which allows it to approximate arbitrary monotonic regression function shapes, and has a built-in covariate selection property. We study the performance of the proposed approach through extensive simulation studies, and demonstrate its practical application in two real data examples.