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

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

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 42 (2008)
Issue (Month): 4 (May)
Pages: 381-394

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Handle: RePEc:eee:transb:v:42:y:2008:i:4:p:381-394

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References

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  1. Monfort, Alain, 1991. "Exogenous and Endogenous Sampling," Econometric Theory, Cambridge University Press, vol. 7(03), pages 417-417, September.
  2. Morgenthaler, S. & Vardi, Y., 1986. "Choice-based samples : A non-parametric approach," Journal of Econometrics, Elsevier, vol. 32(1), pages 109-125, June.
  3. White, Halbert, 1987. "A Misspecified Model," Econometric Theory, Cambridge University Press, vol. 3(02), pages 306-306, April.
  4. 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.
  5. Imbens, G.W., 1990. "An Efficient Method Of Moments Estimator For Descrete Choice Models With Choice-Based Sampling," Papers 9009, Tilburg - Center for Economic Research.
  6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  7. Monfort, Alain, 1996. "A Reappraisal of Misspecified Econometric Models," Econometric Theory, Cambridge University Press, vol. 12(04), pages 597-619, October.
  8. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-88, November.
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Citations

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Cited by:
  1. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
  2. Kelchtermans, Stijn & Verboven, Frank, 2007. "Reducing Product Diversity in Higher Education," CEPR Discussion Papers 6508, C.E.P.R. Discussion Papers.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Balz R. Bodenmann, 2011. "Modelling firm (re-)location choice in UrbanSim," ERSA conference papers ersa11p1091, European Regional Science Association.
  8. 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.
  9. 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.
  10. 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.
  11. Christopher Ksoll, 2007. "Family Networks and Orphan Caretaking in Tanzania," Economics Series Working Papers 361, University of Oxford, Department of Economics.
  12. 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.
  13. 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.

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