cmmprobit fits multinomial probit (MNP) models to discrete choice data. cmmprobit allows several correlation structures for the alternatives, including completely unstructured, where all possible correlations are estimated. It also allows for either heteroskedastic or homoskedastic variances among the alternatives and allows arbitrary patterns within the alternative variances or correlations. cmmprobit makes specifying both case-specific and alternative-in-case-specific regressors easy.
The coefficients from multinomial probit are difficult to interpret, but margins allows you to easily estimate effects and test hypotheses of interest. See [CM] Intro 1.
estat provides additional statistics and results:
Predicted statistics after cmmprobit include the linear predictor, the probability that an alternative is selected, and the standard error of the linear predictor.
mprobit also fits multinomial probit models to categorical data but in the simplified situation of having only case-specific covariates (as with the multinomial logistic regression, mlogit). Maximizing the likelihood is much faster in such cases because the numerical approximation to the likelihood is simpler. See [R] mprobit.