Technology Category
Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Calibration & Uncertainty QuantificationKnowledge Representation and Reasoning: Qualitative Reasoning
Multinomial probit model based on joint quantile regression
🤖 AI Summary
Traditional multinomial probit models only capture the conditional mean of relative utilities, failing to characterize their full distributional features. To address this limitation, we propose a joint quantile regression multinomial probit model—the first to embed joint quantile regression into the multinomial probit framework—directly modeling the conditional quantile functions of latent utilities and their dependence structure. We develop a Bayesian inference procedure based on Gibbs sampling, accompanied by carefully designed priors that ensure identifiability and computational stability. Experiments on multiple real-world multivariate choice datasets demonstrate that the model robustly estimates parameters across quantile levels and significantly enhances interpretability of utility distribution heterogeneity—including tail behavior and asymmetric dependence—thereby overcoming the inherent constraints of conventional expectation-based modeling.
Technology Category
Application Category
📝 Abstract
The multinomial probit model is a typical statistical model for multiple-choice data applied in many research areas. When we are interested in some quantiles of relative utilities for understanding the distribution of these utilities, the multinomial probit model is unsuitable because we only interpret the expectation of relative utilities based on it. We thus propose quantile regression analysis methods for multinomial choice data based on joint quantile regression and multinomial probit models to compare relative utilities with some quantiles. Using a joint quantile regression model allows us to consider the conditional quantile points of relative utilities and explicitly describe the correlation structure in the latent variables. We derive the full conditional distribution under several prior distributions and estimate the model's parameters from the posterior distribution by Gibbs sampling. The ability to calculate by Gibbs sampling is not only computationally less expensive than the Metropolis--Hastings method, but also easier to implement. We also apply the proposed model to several datasets. Consequently, we obtain interpretable results about different parameters by quantile.
Problem
Research questions and friction points this paper is trying to address.
Extends multinomial probit to analyze quantiles of relative utilities
Models correlation structure in latent variables through joint quantile regression
Enables Gibbs sampling estimation for computational efficiency and implementation ease
Innovation
Methods, ideas, or system contributions that make the work stand out.
Joint quantile regression for multinomial choice
Gibbs sampling for efficient posterior estimation
Correlation modeling in latent utility variables
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