Numerical Experiments with AMLET, a New Monte-Carlo
              Algorithm for Estimating Mixed Logit Models

           Fabian Bastin,Cinzia Cirillo, Philippe L. Toint
                   GRT, Dept Maths, FUNDP, Namur
                         Report 03/10   

Researchers  and  analysts  are  increasingly  using mixed  logit  models  for
estimating  responses to  forecast demand  and to  determine the  factors that
affect individual choices. These models are interesting in that they allow for
taste variations between individuals and  they do not exhibit the independence
from irrelevant  alternatives property. However the  numerical cost associated
to their evaluation can be prohibitive, the inherent probability choices being
represented  by multidimensional  integrals. This  cost remains  high  even if
Monte-Carlo  techniques  are used  to  estimate  those  integrals. This  paper
describes a new algorithm that  uses Monte-Carlo approximations in the context
of  modern trust-region  techniques,  but  also exploits  new  results on  the
convergence  of accuracy  and  bias estimators  to  considerably increase  its
numerical efficiency.  Numerical experiments are presented  for both simulated
and real data.   They indicate that the new algorithm  is very competitive and
compares   favourably  with  existing   tools,  including   quasi  Monte-Carlo
techniques based on Halton sequences.