Bayesian Nonparametric Modeling for Multivariate Ordinal Regression

TL;DR

This paper introduces a Bayesian nonparametric approach for multivariate ordinal regression that offers flexible inference without the limitations of traditional parametric models, demonstrated through econometric data applications.

Contribution

The paper develops a novel mixture modeling framework for ordinal regression that avoids linearity assumptions and computational challenges of standard models.

Findings

Flexible inference for ordinal responses achieved

Full support of the nonparametric model established

Successful application to econometric data sets

Abstract

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate and multivariate ordinal regression, which is based on mixture modeling for the joint distribution of latent responses and covariates. The modeling framework enables highly flexible inference for ordinal regression relationships, avoiding assumptions of linearity or additivity in the covariate effects. In standard parametric ordinal regression models, computational challenges arise from identifiability constraints and estimation of parameters requiring nonstandard inferential techniques. A key feature of the nonparametric model is that it achieves inferential flexibility, while avoiding these difficulties. In particular, we establish full support of the nonparametric mixture model under fixed cut-off points that relate through discretization the latent continuous responses with the ordinal responses. The practical utility of the modeling approach is illustrated through application to two data sets from econometrics, an example involving regression relationships for ozone concentration, and a multirater agreement problem.