Testing the Multinomial Logit Model against the Multinomial Probit Model without Estimating the Probit Parameters

The multinomial logit formulation of travel demand models is analytically transparent and computationally tractable, but it is based on relatively restrictive behavioral assumptions. The validity of these assumptions for a given choice situation can be tested empirically by comparing the logit model with a general multinomial probit model. This paper describes a Lagrangian multiplier test that enables the comparison to be carried out without estimating the values of the parameters of a general probit model.