Application of an adaptive Monte-Carlo algorithm
                      to mixed logit estimation

                 F. Bastin, C. Cirillo, Ph. L. Toint

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
approximate the values of this  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 is
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, in both  cases, with that of existing tools using low
discrepancy sequences.