In general for the multinomial discrete choice models in MDC, the predicted value is the probability that the alternative is chosen, conditional on the the model, the parameter estimates, and the covariates. For individual i and alternative j this is given by:
pred_ij = P( U_ij > U_ik for all k not equal to j)
where U_ik is the estimated utility for individual i for alternative j. For multinomial probit, these probabilities cannot be computed in closed form. So instead, MDC simulates from the joint distribution of i's utilities, and uses that simulation to approximate the predicted probabilities. Simulation is easy because the vector of utilities are multivariate normal distributed with a known mean vector (given by the xbetas), and a known covariance matrix (given by the estimate of Sigma). The particular simulation technique MDC uses is known as the GHK simulator. The MDC documentation has some references discussing the GHK simulator that you can read for more information:
Geweke, J. (1989). “Bayesian Inference in Econometric Models Using Monte Carlo Integration.” Econometrica 57:1317–1339.
Hajivassiliou, V. A. (1993). “Simulation Estimation Methods for Limited Dependent Variable Models.” In Econometrics, edited by G. S. Maddala, C. R. Rao, and H. D. Vinod. Vol. 11 of Handbook of Statistics, 519–543. New York: Elsevier Science.
Keane, M. P. (1994). “A Computationally Practical Simulation Estimator for Panel Data.” Econometrica 62:95–116.
Hajivassiliou, V. A., McFadden, D. L., and Ruud, P. A. (1996). “Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives: Theoretical and Computational Results.” Journal of Econometrics 72:85–134
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