Estimating nonparametric random utility models with an application to the value of time in heterogeneous populations

Fabian Bastin, Cinzia Cirillo, Philippe Toint

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The estimation of random parameters by means of mixed logit models is now current practice for the analysis of transportation behaviour. One of the most straightforward applications is the derivation of willingnessto- pay distribution over a heterogeneous population, an important element for dynamic tolling strategies on congested networks. In numerous practical cases, the underlying discrete choice models involve parametric distributions that are a priori specified and whose parameters are estimated. This approach can however lead to many problems for realistic interpretation, such as negative value of time, etc. 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 nonparametric random vectors is tested. The nonparametric mixed logit model is also used on real data derived from a stated preference survey conducted in the region of Brussels (Belgium). The model presents multiple choices and is estimated on repeated observations. The obtained results provide a more realistic interpretation of the observed behaviours. © 2010 INFORMS.
Original languageEnglish
Pages (from-to)537-549
Number of pages13
JournalTransportation Science
Issue number4
Publication statusPublished - 1 Nov 2010


  • discret-choice models
  • numerical estimation.
  • Stochastic programming
  • nonparametric distributions


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