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We develop a nonparametric Bayesian modeling approach to ordinal regressionbased on priors placed directly on the discrete distribution of the ordinalresponses. The prior probability models are built from a structured mixture ofmultinomial distributions. We leverage a continuation-ratio logitsrepresentation to formulate the mixture kernel, with mixture weights definedthrough the logit stick-breaking process that incorporates the covariatesthrough a linear function. The implied regression functions for the responseprobabilities can be expressed as weighted sums of parametric regressionfunctions, with covariate-dependent weights. Thus, the modeling approachachieves flexible ordinal regression relationships, avoiding linearity oradditivity assumptions in the covariate effects. A key model feature is thatthe parameters for both the mixture kernel and the mixture weights can beassociated with a continuation-ratio logits regression structure. Hence, anefficient and relatively easy to implement posterior simulation method can bedesigned, using P\'olya-Gamma data augmentation. Moreover, the model is builtfrom a conditional independence structure for category-specific parameters,which results in additional computational efficiency gains through partialparallel sampling. In addition to the general mixture structure, we studysimplified model versions that incorporate covariate dependence only in themixture kernel parameters or only in the mixture weights. For all proposedmodels, we discuss approaches to prior specification and develop Markov chainMonte Carlo methods for posterior simulation. The methodology is illustratedwith several synthetic and real data examples.

Structured Mixture of Continuation-ratio Logits Models for Ordinal Regression