Analytic approximations for computing probit choice probabilities

The multinomial probit model has long been used in transport applications as the basis for mode- and route-choice in computing network flows, and in other choice contexts when estimating preference parameters. It is well known that computation of the probit choice probabilities presents a significant computational burden, since they are based on multivariate normal integrals. Various methods exist for computing these choice probabilities, though standard Monte Carlo is most commonly used. In this article we compare two analytical approximation methods (Mendell-Elston and Solow-Joe) with three Monte Carlo approaches for computing probit choice probabilities. We systematically investigate a wide range of parameter settings and report on the accuracy and computational efficiency of each method. The findings suggest that the accuracy and efficiency of an optimally ordered Mendell-Elston analytic approximation method offers great potential for wider use.