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

Abstract

This
\npaper proposes the use of a quasi-random sequence for the estimation of the mixed
\nmultinomial
\nlogit model. The mixed multinomial structure is a flexible discrete choice formulation
\nwhich
\naccommodates general patterns of competitiveness as well as heterogeneity across
\nindividuals
\nin sensitivity to exogenous variables. The estimation of this model has been achieved
\nin
\nthe past using the pseudo-random maximum simulated likelihood method that evaluates the
\nmulti-dimensional integrals in the log-likelihood function by computing the integrand at a sequence
\nof
\npseudo-random points and taking the average of the resulting integrand value. We suggest and
\nimplement an alternative quasi-random maximum simulated likelihood method which uses cleverly
\ncrafted
\nnon-random but more uniformly distributed sequences in place of the pseudo-random
\npoints
\nin the estimation of the mixed logit model. Numerical experiments, in the context of
\nintercity
\ntravel mode choice, indicate that the quasi-random method provides considerably better
\naccuracy with much fewer
\ndraws and computational time than does the pseudo-random method. This
\nresult has the potential to dramatically influence the use of the mixed logit model in practice;
\nspecifically,
\ngiven the flexibility of the mixed logit model, the use of the quasi-random estimation
\nmethod
\nshould facilitate the application of behaviorally rich structures in discrete choice modeling.