A Symmetric Prior for Multinomial Probit Models

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is to uniquely identify parameters model. This paper proposes novel identification strategy, and associated prior distribution for model parameters, that renders symmetric with respect relabeling outcome categories. The new permits an efficient Gibbs algorithm samples rank-deficient covariance matrices without resorting Metropolis-Hastings updates.