Estimating mixed logit
with non-parametric random variables
F. Bastin, C. Cirillo and Ph. L. Toint
Report 06/05
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 an heterogeneous population. In many 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, unboundd distributions often produce value
ranges with difficult behavioural interpretation. Thirdly, littel is known
about the tails and their effetcts on the meanb of the estimates (Hess
et. al. 2005, Cirillo and Axhausen, 2006).
The paper extends the nonparametric methods in a classical context of mixed
logit models. The random variables of the objective functions are assumed to
be continuous, bounded and independent, and we are interested by the inverse
distribution functions. These functions are modeled by means of cubic
B-splines with strictly increasing base coesfficients, a sufficient condition
to construct monotonic (increasing) functions. As a result, the number of
parameters that have to be estimated increases; the information on the tails
and on the shape of the random variables however should help the analyst to
find the right parametric distribution for the random parameters (iy it
exists).
The technique is applied to simulated data and the ability to recover both
parametric and nonparametric random vectors is tested. The nonparametric
mixed logit model is also used on real data derived froma survey on electric
car, whose prototype has been realized and tested in a number of cities in
Europe. The data set, which is part of a European study called "Cybercar" is
a stated preference experiment conducted in Brussels in 2002. The model
presents multiple choices and is estimated on repeated observations.