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The multinomial probit (MNP) model is a useful tool for describingdiscrete-choice data and there are a variety of methods for fitting the model.Among them, the algorithms provided by Imai and van Dyk (2005a), based onMarginal Data Augmentation, are widely used, because they are efficient interms of convergence and allow the possibly improper prior distribution to bespecified directly on identifiable parameters. Burgette and Nordheim (2012)modify a model and algorithm of Imai and van Dyk (2005a) to avoid an arbitrarychoice that is often made to establish identifiability. There is an error inthe algorithms of Imai and van Dyk (2005a), however, which affects both theiralgorithms and that of Burgette and Nordheim (2012). This error can alter thestationary distribution and the resulting fitted parameters as well as theefficiency of these algorithms. We propose a correction and use both asimulation study and a real-data analysis to illustrate the difference betweenthe original and corrected algorithms, both in terms of their estimatedposterior distributions and their convergence properties. In some cases, theeffect on the stationary distribution can be substantial.

A Corrected and More Efficient Suite of MCMC Samplers for the Multinomal Probit Model