Chapter 3 - Bayesian nonparametric density regression for ordinal responses

Abstract

We present a Bayesian nonparametric model for ordinal responses, which is based on mixture modelling for the joint distribution of covariates and latent continuous responses. The modelling framework enables flexible inference for both the regression relationships and other aspects of the conditional response distribution. In typical ordinal regression models, assumptions include linearity and parametric distributions. These assumptions may be restrictive for many applications, and computational challenges arise when fitting these models. The nonparametric ordinal regression model avoids these challenges. This modelling approach falls into the class of Bayesian nonparametric density regression methods, which we also review. The density regression modelling approach is illustrated with both continuous and ordinal responses through an application to estimate the relationships between ozone concentration and other environmental characteristics.