  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.

Methodology