MultiprocessMultilevel Modeling aML |
## Likelihood and Predictions of Multinomial Probit ModelThis note describes how to calculate the likelihood of a multinomial probit. By trivial extension, it permits calculating the predicted probabilities of an estimated multinomial probit model.Consider a binomial probit with potential outcomes All three probabilities involve a cumulative bivariate normal probability. The first is trivial: . For the others, we first need to determine the bivariate covariance matrices. The covariance matrix for is and thus . The last covariance matrix is and thus . Internally, aML Version 2.0 follows a generalized version of the above
discussion: it converts every The likelihood and predicted probabilities may readily be estimated using any
statistical package that supports the bivariate cumulative normal probability
function. We illustrate the implementation in Stata with ado file
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