Improved Algorithms for Estimating Choice Probabilities in the Multinomial Probit Model

One of the problems in the application of multinomial probit models has been the lack of a satisfactory algorithm for estimating choice probabilities. The currently used “Clark” method meets most of the requirements, but is subject to errors which are occasionally unacceptably large. This paper describes a new algorithm which, at the expense of some additional complexity, produces estimates of choice probability which never have large errors. This “separated split” method has many similarities to the Clark method, but employs a different type of recursive structure. Examination of higher moments of intermediate utility distributions has enabled an upper limit to be set on the possible size of error for problems with three choice alternatives. A new “correlated logit” choice model has also been developed, which uses the same recursive structure as the separated split. Multinomial Probit model, but assumes an invariant covariance matrix. It has been found to give a surprisingly good approximation to the exact MNP model for problems with up to six choice alternatives, in many cases producing smaller errors than the Clark method. Under appropriate conditions it condenses to become identical to the well known hierarchical logit model.