Multinomial probit with structured covariance for route choice behavior

We propose another version of the multinomial probit model with a structured covariance matrix to represent any overlapped relation between route alternatives. The fundamental ideas of the model were presented in Yai et al. (1993) and Yai and Iwakura (1994). The assumptions introduced in the model may be more realistic for route choice behaviors on a dense network than the strict assumption of the independent alternative property of the multinomial logit model. As the nested logit model assumes an identical dispersion parameter between two modeling levels for all trip makers, the model has difficulty in expressing individual choice-tree structures. To improve the applicability of the multinomial probit model to route choice behaviors, we introduce a function which represents an overlapped relation between pairs of alternatives and propose a multinomial probit model in which the structured covariance matrix uses the function in order to consider the individual choice-tree structures in the matrix and the estimatability of the new alternative's covariances. After examining the applicability of the multinomial probit model using empirical route choice data in a Tokyo metropolitan region, we also propose a method for evaluating consumer benefits on complicated networks based on the multinomial probit model.