Fast Variational Bayes Methods for Multinomial Probit Models

The multinomial probit model is often used to analyze choice behavior. However, estimation with existing Markov chain Monte Carlo (MCMC) methods computationally costly, which limits its applicability large datasets. This article proposes a variational Bayes method that accurate and fast, even when number of alternatives observations are considered. Variational usually require an analytical expression for the unnormalized posterior density adequate family. Both challenging specify in probit, has requires identifying restrictions augmented set latent utilities. We employ spherical transformation on covariance matrix utilities construct identifies parameters, use conditional as part proposed faster than MCMC, can be made scalable both observations. accuracy scalability our illustrated numerical experiments real purchase data one million