IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v44y2010i4p537-549.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1100.0321
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1100.0321?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    5. 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.
    6. 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.
    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. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Daly, Andrew, 1982. "Estimating choice models containing attraction variables," Transportation Research Part B: Methodological, Elsevier, vol. 16(1), pages 5-15, February.
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vij, Akshay & Krueger, Rico, 2017. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 76-101.
    2. 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.
    3. 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).
    4. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Bazzani, Claudia & Palma, Marco A. & Nayga, Rodolfo M., Jr., 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), April.
    13. 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).
    14. 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.
    15. 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.
    16. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    17. 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.
    18. 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.
    19. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tabasi, Maliheh & Rose, John M. & Pellegrini, Andrea & Hossein Rashidi, Taha, 2024. "An empirical investigation of the distribution of travellers’ willingness-to-pay: A comparison between a parametric and nonparametric approach," Transport Policy, Elsevier, vol. 146(C), pages 312-321.
    2. Fosgerau, Mogens & Hess, Stephane, 2008. "Competing methods for representing random taste heterogeneity in discrete choice models," MPRA Paper 10038, University Library of Munich, Germany.
    3. Bliemer, Michiel C.J. & Rose, John M., 2013. "Confidence intervals of willingness-to-pay for random coefficient logit models," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 199-214.
    4. Kalouptsidis, N. & Psaraki, V., 2010. "Approximations of choice probabilities in mixed logit models," European Journal of Operational Research, Elsevier, vol. 200(2), pages 529-535, January.
    5. De Ayala Bilbao, Amaya & Hoyos Ramos, David & Mariel Chladkova, Petr, 2012. "Landscape valuation through discrete choice experiments: Current practice and future research reflections," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    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. Stephane Hess, 2014. "Latent class structures: taste heterogeneity and beyond," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 14, pages 311-330, Edward Elgar Publishing.
    8. Small, Kenneth A., 2012. "Valuation of travel time," Economics of Transportation, Elsevier, vol. 1(1), pages 2-14.
    9. Börjesson, Maria & Eliasson, Jonas, 2014. "Experiences from the Swedish Value of Time study," Transportation Research Part A: Policy and Practice, Elsevier, vol. 59(C), pages 144-158.
    10. Hong, Sung-Pil & Kim, Kyung min & Byeon, Geunyeong & Min, Yun-Hong, 2017. "A method to directly derive taste heterogeneity of travellers’ route choice in public transport from observed routes," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 41-52.
    11. Hoyos, David, 2010. "The state of the art of environmental valuation with discrete choice experiments," Ecological Economics, Elsevier, vol. 69(8), pages 1595-1603, June.
    12. Daziano, Ricardo A. & Achtnicht, Martin, 2014. "Accounting for uncertainty in willingness to pay for environmental benefits," Energy Economics, Elsevier, vol. 44(C), pages 166-177.
    13. Börjesson, Maria & Fosgerau, Mogens & Algers, Staffan, 2012. "Catching the tail: Empirical identification of the distribution of the value of travel time," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(2), pages 378-391.
    14. Poudel, Niranjan & Singleton, Patrick A., 2024. "Willingness to pay for changes in travel time and work time: A stated choice experiment of US commuters," Research in Transportation Economics, Elsevier, vol. 103(C).
    15. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    16. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
    17. 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.
    18. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    19. Hoyos Ramos, David, 2010. "Using discrete choice experiments for environmental valuation," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    20. Jie Yu & Peter Goos & Martina Vandebroek, 2009. "Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity," Marketing Science, INFORMS, vol. 28(1), pages 122-135, 01-02.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:44:y:2010:i:4:p:537-549. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.