A Multinomial Probit Model for Asymmetric Choice Responses

2026-08-10

AI Summary

This study addresses a key limitation of traditional multinomial probit models, which assume symmetric latent utility distributions and thus fail to capture asymmetric effects of covariates on choice probabilities, leading to biased estimates of elasticities and substitution patterns. To overcome this, the paper proposes the first identifiable and computationally tractable skew multinomial probit (SMNP) model. By incorporating a multivariate skew-normal distribution with alternative-specific skewness parameters, the model captures asymmetric responses while preserving flexible substitution structures. Model identification and covariance matrix positive definiteness are ensured through a novel reparameterization. Efficient Bayesian inference is achieved via an interpretable prior specification and a Metropolis–Hastings-within-Gibbs sampler augmented with dual data augmentation. Both simulation studies and empirical applications demonstrate that the SMNP model substantially improves predictive accuracy for choice probabilities and reveals economically meaningful asymmetries in price elasticities and substitution behavior.

Abstract

Standard multinomial probit (MNP) models specify symmetric latent utility distributions, implying that choice probabilities respond symmetrically to positive and negative covariate shifts of the same magnitude. This restriction is often implausible in empirical choice settings and can lead to misleading elasticity and substitution predictions. We propose a skewed multinomial probit (SMNP) model that captures asymmetric choice responses by specifying a multivariate skew-normal distribution for the latent utilities. The model preserves the flexible substitution patterns of the MNP framework, introduces alternative-specific skewness parameters, and nests the standard MNP model when skewness is zero. Introducing skewness creates identification and computational challenges because the skewness parameters interact with the MNP scale normalization and disrupt the conditional Gaussian updating structure used in Bayesian MNP estimation. We address these challenges through a covariance reparameterization that enforces identification and positive definiteness by construction, interpretable priors on the identified parameter space, and a double data-augmentation scheme that yields a Metropolis-Hastings within Gibbs sampler. Numerical experiments and applications to consumer choice data show that SMNP recovers asymmetric choice responses, improves probabilistic prediction, and produces economically meaningful differences in price elasticities and substitution patterns.

Problem

• multinomial probit
• asymmetric choice responses
• skewness
• latent utility
• choice modeling

Innovation

• skewed multinomial probit
• asymmetric choice responses
• multivariate skew-normal distribution
• Bayesian estimation
• data augmentation