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Abstract:
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Traditionally, ordinal responses are assumed to arise through discretization of a latent continuous distribution, with covariate effects entering linearly. This approach limits the covariate-response relationship and faces computational challenges. We develop a novel Bayesian nonparametric modeling approach to ordinal regression based on priors placed directly on the discrete distribution of the ordinal responses. The prior probability model is built from a structured mixture of multinomial distributions. We leverage a continuation-ratio logits representation and Pólya-Gamma augmentation to formulate the mixture kernel, with mixture weights defined through the logit stick-breaking process that allows the covariates to enter through a linear function. The implied regression functions for the response probabilities can be expressed as weighted sums of regression functions under traditional parametric models, with covariate-dependent weights. Thus, the modeling approach achieves flexibility in ordinal regression relationships, avoiding linearity or additivity assumptions in the covariate effects. The methodology is illustrated with several synthetic and real data examples.
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