A Symmetric Prior for Multinomial Probit Models
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Under standard prior distributions, fitted probabilities from Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to identify the model. This paper proposes a novel identification strategy and prior distribution for the model parameters that makes the prior symmetric with respect to relabeling the outcome categories. Further, our new prior allows an efficient Gibbs algorithm that samples rank-deficient covariance matrices without resorting to Metropolis-Hastings updates.
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