As such, it is an alternative to the multinomial logit model as one method of multiclass classification.
Some examples: The multinomial probit model is a statistical model that can be used to predict the likely outcome of an unobserved multi-way trial given the associated explanatory variables.
That is: or equivalently for each of m possible values of h. Multinomial probit is often written in terms of a latent variable model: where Then That is, Note that this model allows for arbitrary correlation between the error variables, so that it doesn't necessarily respect independence of irrelevant alternatives.
is the identity matrix (such that there is no correlation or heteroscedasticity), the model is called independent probit.
For details on how the equations are estimated, see the article Probit model.