Estimating non-parametric random utility models, 
                 with an application  to the value of time 
                       in heterogeneous populations

            Fabian Bastin   Cinzia Cirillo   Philippe L. Toint

                             Report TR07/15

The estimation of random parameters by means of mixed logit models is becoming
current  practice   amongst  discrete  choice   analysts,  one  of   the  most
straightforward  applications  being  the  derivation of  willingness  to  pay
distribution  over a  heterogeneous population.  In numerous  practical cases,
parametric distributions are  a priori specified and the  parameters for these
distributions are estimated. This approach  can however lead to many practical
problems. Firstly,  it is  difficult to assess  which is the  more appropriate
analytical  distribution.  Secondly,  unbounded  distributions  often  produce
values ranges  with difficult  behavioural interpretation. Thirdly,  little is
known about the  tails and their effects on the mean  of the estimates. (Hess,
Bierlaire, Polak, 2005, Cirillo and Axhausen, 2006).

In this  paper, we propose to capture  the randomness present in  the model by
using a  new nonparametric  estimation method, based  on the  approximation of
inverse  cumulative  distribution functions.   This  technique  is applied  to
simulated data and  the ability to recover both  parametric and non-parametric
random vectors is tested. The non-parametric mixed logit model is also used on
real data derived  from a Stated Preference survey conducted  in the region of
Brussels  (Belgium) in  2002.   The  model presents  multiple  choices and  is
estimated on repeated observations.