## Multinomial Probit Model

Let Uj, j = 0, 1, 2,. . ., m, be the stochastic utility associated with the yth alternative for a particular individual. By the multinomial probit model, we mean the model in which {Uj) are jointly normally distributed. Such a model was first proposed by Aitchison and Bennett (1970). This model has rarely been used in practice until recently because of its computational difficulty (except, of course, when m = 1, in which case the model is reduced to a binary

probit model, which is discussed in Section 9.2). To illustrate the complexity of the problem, consider the case of m = 2. Then, to evaluate P(y = 2), for example, we must calculate the multiple integral

P(y~L) = P(U2 > Ul, U2> U0)

where / is a trivariate normal density...

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