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

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  • Fabian Bastin

    (Department of Computing Science and Operational Research, University of Montréal, Montréal, Québec H3C 3J7, Canada, and CIRRELT, Department of Computing Science and Operational Research, University of Montréal, Montréal, Québec H3C 3J7, Canada)

  • Cinzia Cirillo

    (Department of Civil and Environmental Engineering, University of Maryland, College Park, Maryland 20742)

  • Philippe L. Toint

    (Department of Mathematics, University of Namur, B5000 Namur, Belgium)

Abstract

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 willingness-to-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.

Suggested Citation

  • Fabian Bastin & Cinzia Cirillo & Philippe L. Toint, 2010. "Estimating Nonparametric Random Utility Models with an Application to the Value of Time in Heterogeneous Populations," Transportation Science, INFORMS, vol. 44(4), pages 537-549, November.
    • Handle: RePEc:inm:ortrsc:v:44:y:2010:i:4:p:537-549
    DOI: 10.1287/trsc.1100.0321
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    4. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models," Journal of choice modelling, Elsevier, vol. 27(C), pages 97-113.
    5. Weibo Li & Maria Kamargianni, 2020. "An Integrated Choice and Latent Variable Model to Explore the Influence of Attitudinal and Perceptual Factors on Shared Mobility Choices and Their Value of Time Estimation," Transportation Science, INFORMS, vol. 54(1), pages 62-83, January.
    6. Munger, D. & L’Ecuyer, P. & Bastin, F. & Cirillo, C. & Tuffin, B., 2012. "Estimation of the mixed logit likelihood function by randomized quasi-Monte Carlo," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 305-320.
    7. Claudia Bazzani & Marco A. Palma & Rodolfo M. Nayga, 2018. "On the use of flexible mixing distributions in WTP space: an induced value choice experiment," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 62(2), pages 185-198, April.
    8. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    9. Riccardo Scarpa & Cristiano Franceschinis & Mara Thiene, 2017. "A Monte Carlo Evaluation of the Logit-Mixed Logit under Asymmetry and Multimodality," Working Papers in Economics 17/23, University of Waikato.
    10. Daziano, Ricardo A., 2020. "Flexible customer willingness to pay for bundled smart home energy products and services," Resource and Energy Economics, Elsevier, vol. 61(C).
    11. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    12. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    13. Czajkowski, Mikołaj & Budziński, Wiktor, 2019. "Simulation error in maximum likelihood estimation of discrete choice models," Journal of choice modelling, Elsevier, vol. 31(C), pages 73-85.
    14. S. Van Cranenburgh & S. Wang & A. Vij & F. Pereira & J. Walker, 2021. "Choice modelling in the age of machine learning -- discussion paper," Papers 2101.11948, arXiv.org, revised Nov 2021.
    15. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Extending the logit-mixed logit model for a combination of random and fixed parameters," Journal of choice modelling, Elsevier, vol. 27(C), pages 88-96.
    16. Caputo, Vincenzina & Scarpa, Riccardo & Nayga, Rodolfo M. & Ortega, David L., 2018. "Are preferences for food quality attributes really normally distributed? An analysis using flexible mixing distributions," Journal of choice modelling, Elsevier, vol. 28(C), pages 10-27.
    17. Rico Krueger & Taha H. Rashidi & Akshay Vij, 2019. "Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services," Papers 1907.09639, arXiv.org.
    18. Steven M. Ramsey & Jason S. Bergtold, 2021. "Examining Inferences from Neural Network Estimators of Binary Choice Processes: Marginal Effects, and Willingness-to-Pay," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1137-1165, December.
    19. Chandra R. Bhat & Patrícia S. Lavieri, 2018. "A new mixed MNP model accommodating a variety of dependent non-normal coefficient distributions," Theory and Decision, Springer, vol. 84(2), pages 239-275, March.

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