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

Author

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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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    as
    1. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    2. Cascetta, Ennio & Russo, Francesco & Viola, Francesco A. & Vitetta, Antonino, 2002. "A model of route perception in urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 577-592, August.
    3. Joel Huber and Kenneth Train., 2000. "On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths," Economics Working Papers E00-289, University of California at Berkeley.
    4. Bhat, Chandra R., 1998. "Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 495-507, September.
    5. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
    6. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    7. Sivaramakrishnan Srinivasan & Chandra Bhat, 2005. "Modeling household interactions in daily in-home and out-of-home maintenance activity participation," Transportation, Springer, vol. 32(5), pages 523-544, September.
    8. Daly, Andrew, 1982. "Estimating choice models containing attraction variables," Transportation Research Part B: Methodological, Elsevier, vol. 16(1), pages 5-15, February.
    9. Cirillo, C. & Axhausen, K.W., 2006. "Evidence on the distribution of values of travel time savings from a six-week diary," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(5), pages 444-457, June.
    10. Helen X.H. Bao & Alan T.K. Wan, 2004. "On the Use of Spline Smoothing in Estimating Hedonic Housing Price Models: Empirical Evidence Using Hong Kong Data," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 32(3), pages 487-507, September.
    11. Proussaloglou, Kimon & Koppelman, Frank S., 1999. "The choice of air carrier, flight, and fare class," Journal of Air Transport Management, Elsevier, vol. 5(4), pages 193-201.
    12. Hess, Stephane & Bierlaire, Michel & Polak, John W., 2005. "Estimation of value of travel-time savings using mixed logit models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 221-236.
    13. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    14. David Hensher, 2006. "The Signs of the Times: Imposing a Globally Signed Condition on Willingness to Pay Distributions," Transportation, Springer, vol. 33(3), pages 205-222, May.
    15. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    16. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
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    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    9. 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.
    10. 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.
    11. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    12. 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.
    13. Zhang, Jian & Nault, Barrie R. & Tu, Yiliu, 2015. "A dynamic pricing strategy for a 3PL provider with heterogeneous customers," International Journal of Production Economics, Elsevier, vol. 169(C), pages 31-43.
    14. Laura Eboli & Gabriella Mazzulla, 2014. "Investigating the heterogeneity of bus users' preferences through discrete choice modelling," Transportation Planning and Technology, Taylor & Francis Journals, vol. 37(8), pages 695-710, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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