Application of an adaptive Monte Carlo algorithm to mixed logit estimation

This paper presents the application of a new algorithm for maximizing the simulated likelihood functions appearing in the estimation of mixed multinomial logit (MMNL) models. The method uses Monte Carlo sampling to produce the approximate likelihood function and dynamically adapts the number of draws on the basis of statistical estimators of the simulation error and simulation bias. Its convergence from distant starting points is ensured by a trust-region technique, in which improvement is ensured by locally maximizing a quadratic model of the objective function. Simulated data are first used to assess the quality of the results obtained and the relative performance of several algorithmic variants. These variants involve, in particular, different techniques for approximating the model's Hessian and the substitution of the trust-region mechanism by a linesearch. The algorithm is also applied to a real case study arising in the context of a recent Belgian transportation model. The performance of the new Monte Carlo algorithm is shown to be competitive with that of existing tools using low discrepancy sequences. © 2005 Elsevier Ltd. All rights reserved.