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The estimation of generalized extreme value models from choice-based samples


  • Bierlaire, M.
  • Bolduc, D.
  • McFadden, D.


In the presence of choice-based sampling strategies for data collection, the property of multinomial logit (MNL) models, that consistent estimates of all parameters but the constants can be obtained from an exogenous sample maximum likelihood (ESML) estimation, does not hold in general for generalized extreme value (GEV) models. We propose a consistent ESML estimator for GEV models in this context. We first identify a specific class of GEV models with the desired property that, similarly to MNL, the constants absorb the potential bias. We then propose a new and simple weighted conditional maximum likelihood (WCML) estimator for the more general case. Contrarily to the weighted exogenous sample maximum likelihood (WESML) estimator by Manski and Lerman [Manski, C., Lerman, S., 1977. The estimation of choice probabilities from choice-based samples. Econometrica 45, 1977-1988], the new WCML estimator does not require an external knowledge of the market shares. We show that this applies also to the case where alternatives are sampled from a large choice set, and we illustrate the use of the estimator on synthetic and real data.

Suggested Citation

  • Bierlaire, M. & Bolduc, D. & McFadden, D., 2008. "The estimation of generalized extreme value models from choice-based samples," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 381-394, May.
  • Handle: RePEc:eee:transb:v:42:y:2008:i:4:p:381-394

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    References listed on IDEAS

    1. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    2. Monfort, Alain, 1992. "Exogenous and Endogenous Sampling," Econometric Theory, Cambridge University Press, vol. 8(03), pages 427-428, September.
    3. White, Halbert, 1987. "A Misspecified Model," Econometric Theory, Cambridge University Press, vol. 3(02), pages 306-306, April.
    4. Monfort, Alain, 1996. "A Reappraisal of Misspecified Econometric Models," Econometric Theory, Cambridge University Press, vol. 12(04), pages 597-619, October.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Daly, Andrew & Bierlaire, Michel, 2006. "A general and operational representation of Generalised Extreme Value models," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 285-305, May.
    7. Morgenthaler, S. & Vardi, Y., 1986. "Choice-based samples : A non-parametric approach," Journal of Econometrics, Elsevier, vol. 32(1), pages 109-125, June.
    8. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-1988, November.
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    Cited by:

    1. Smirnov, Oleg A. & Egan, Kevin J., 2012. "Spatial random utility model with an application to recreation demand," Economic Modelling, Elsevier, vol. 29(1), pages 72-78.
    2. Frejinger, E. & Bierlaire, M. & Ben-Akiva, M., 2009. "Sampling of alternatives for route choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 984-994, December.
    3. Hindsley, Paul & Landry, Craig E. & Gentner, Brad, 2011. "Addressing onsite sampling in recreation site choice models," Journal of Environmental Economics and Management, Elsevier, vol. 62(1), pages 95-110, July.
    4. repec:eee:transa:v:100:y:2017:i:c:p:228-246 is not listed on IDEAS
    5. Andrew Daly, 2013. "Forecasting behaviour: with applications to transport," Chapters,in: Choice Modelling, chapter 2, pages 48-72 Edward Elgar Publishing.
    6. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    7. Lemp, Jason D. & Kockelman, Kara M., 2012. "Strategic sampling for large choice sets in estimation and application," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(3), pages 602-613.
    8. Brian Lee & Paul Waddell, 2010. "Residential mobility and location choice: a nested logit model with sampling of alternatives," Transportation, Springer, vol. 37(4), pages 587-601, July.
    9. Christopher Ksoll, 2007. "Family Networks and Orphan Caretaking in Tanzania," Economics Series Working Papers 361, University of Oxford, Department of Economics.
    10. Andrew Daly, 2014. "Forecasting choice," Chapters,in: Handbook of Choice Modelling, chapter 25, pages 627-646 Edward Elgar Publishing.
    11. Abay, Kibrom A., 2015. "Investigating the nature and impact of reporting bias in road crash data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 71(C), pages 31-45.
    12. Balz R. Bodenmann, 2011. "Modelling firm (re-)location choice in UrbanSim," ERSA conference papers ersa11p1091, European Regional Science Association.
    13. Lai, Xinjun & Bierlaire, Michel, 2015. "Specification of the cross-nested logit model with sampling of alternatives for route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 220-234.
    14. Kelchtermans, Stijn & Verboven, Frank, 2007. "Reducing Product Diversity in Higher Education," CEPR Discussion Papers 6508, C.E.P.R. Discussion Papers.
    15. Pereira, Pedro & Ribeiro, Tiago & Vareda, João, 2013. "Delineating markets for bundles with consumer level data: The case of triple-play," International Journal of Industrial Organization, Elsevier, vol. 31(6), pages 760-773.
    16. Stijn Kelchtermans & Frank Verboven, 2010. "Participation and study decisions in a public system of higher education," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 355-391.
    17. Kelchtermans, Stijn & Verboven, Frank, 2010. "Program duplication in higher education is not necessarily bad," Journal of Public Economics, Elsevier, vol. 94(5-6), pages 397-409, June.
    18. Haghani, Milad & Sarvi, Majid & Shahhoseini, Zahra, 2015. "Accommodating taste heterogeneity and desired substitution pattern in exit choices of pedestrian crowd evacuees using a mixed nested logit model," Journal of choice modelling, Elsevier, vol. 16(C), pages 58-68.
    19. Newman, Jeffrey P. & Ferguson, Mark E. & Garrow, Laurie A., 2013. "Estimating GEV models with censored data," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 170-184.
    20. Guevara, C. Angelo & Ben-Akiva, Moshe E., 2013. "Sampling of alternatives in Multivariate Extreme Value (MEV) models," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 31-52.

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