A practical technique to estimate multinomial probit models in transportation

The Multinomial Probit formulation provides a very general framework to allow for inter-dependent alternatives in discrete choice analysis. Up until recently, its use was rather limited, mainly because of the computational difficulties associated with the evaluation of the choice probabilities which are multidimensional normal integrals. In recent years, the econometric estimation of Multinomial Probit models has greatly been focused on. Alternative simulation based approaches have been suggested and compared. Most approaches exploit a conventional estimation technique where easy to compute simulators replace the choice probabilities. For situations such as in transportation demand modelling where samples and choice sets are large, the existing literature clearly suggests the use of a maximum simulated likelihood framework combined with a Geweke–Hajivassiliou–Keane choice probability simulator. The present paper gives the computational details regarding the implementation of this practical estimation approach where the scores are computed analytically. This represents a contribution of the paper, because usually, numerical derivatives are used. The approach is tested on a 9-mode transportation choice model estimated with disaggregate data from Santiago, Chile.