  The multinomial probit (MNP) model is a useful tool for describing
discrete-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 on
Marginal Data Augmentation, are widely used, because they are efficient in
terms of convergence and allow the possibly improper prior distribution to be
specified directly on identifiable parameters. Burgette and Nordheim (2012)
modify a model and algorithm of Imai and van Dyk (2005a) to avoid an arbitrary
choice that is often made to establish identifiability. There is an error in
the algorithms of Imai and van Dyk (2005a), however, which affects both their
algorithms and that of Burgette and Nordheim (2012). This error can alter the
stationary distribution and the resulting fitted parameters as well as the
efficiency of these algorithms. We propose a correction and use both a
simulation study and a real-data analysis to illustrate the difference between
the original and corrected algorithms, both in terms of their estimated
posterior distributions and their convergence properties. In some cases, the
effect on the stationary distribution can be substantial.
