Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model

Abstract

This paper proposes the use of a quasi-random sequence for the estimation of the mixed multinomial logit model. The mixed multinomial structure is a flexible discrete choice formulation which accommodates general patterns of competitiveness as well as heterogeneity across individuals in sensitivity to exogenous variables. The estimation of this model has been achieved in the past using the pseudo-random maximum simulated likelihood method that evaluates the multi-dimensional integrals in the log-likelihood function by computing the integrand at a sequence of pseudo-random points and taking the average of the resulting integrand values. We suggest and implement an alternative quasi-random maximum simulated likelihood method which uses cleverly crafted non-random but more uniformly distributed sequences in place of the pseudo-random points in the estimation of the mixed logit model. Numerical experiments, in the context of intercity travel mode choice, indicate that the quasi-random method provides considerably better accuracy with much fewer draws and computational time than does the pseudo-random method. This result has the potential to dramatically influence the use of the mixed logit model in practice; specifically, given the flexibility of the mixed logit model, the use of the quasi-random estimation method should facilitate the application of behaviorally rich structures in discrete choice modeling.