Estimating Nonparametric Random Utility Models with an Application to the Value of Time in Heterogeneous Populations

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 [18], Cirillo and Axhausen [6]). 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.