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Activity Number: 268 - SBSS Student Paper Competition II
Type: Topic Contributed
Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #322118
Title: Structured Mixture of Continuation-Ratio Logits Models for Ordinal Regression
Author(s): Jizhou Kang* and Athanasios Kottas
Companies: University of California, Santa Cruz and University of California, Santa Cruz
Keywords: Bayesian nonparametric regression; Dependent Dirichlet process; Logit stick-breaking prior; Markov chain Monte Carlo

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 PĆ³lya-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.

Authors who are presenting talks have a * after their name.

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