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Strategic sampling for large choice sets in estimation and application

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  • Lemp, Jason D.
  • Kockelman, Kara M.
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    Abstract

    Many discrete choice contexts in transportation deal with large choice sets, including destination, route, and vehicle choices. Model estimation with large numbers of alternatives remains computationally expensive. In the context of the multinomial logit (MNL) model, limiting the number of alternatives in estimation by simple random sampling (SRS) yields consistent parameter estimates, but estimator efficiency suffers. In the context of more general models, such as the mixed MNL, limiting the number of alternatives via SRS yields biased parameter estimates. In this paper, a new, strategic sampling scheme is introduced, which draws alternatives in proportion to updated choice-probability estimates. Since such probabilities are not known a priori, the first iteration uses SRS among all available alternatives. The sampling scheme is implemented here for a variety of simulated MNL and mixed-MNL data sets, with results suggesting that the new sampling scheme provides substantial efficiency benefits. Thanks to reductions in estimation error, parameter estimates are more accurate, on average. Moreover, in the mixed MNL case, where SRS produces biased estimates (due to violation of the independence of irrelevant alternatives property), the new sampling scheme appears to effectively eliminate such biases. Finally, it appears that only a single iteration of the new strategy (following the initialization step using SRS) is needed to deliver the strategy’s maximum efficiency gains.

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    File URL: http://www.sciencedirect.com/science/article/pii/S096585641100173X
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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part A: Policy and Practice.

    Volume (Year): 46 (2012)
    Issue (Month): 3 ()
    Pages: 602-613

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    Handle: RePEc:eee:transa:v:46:y:2012:i:3:p:602-613

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    Related research

    Keywords: Multinomial logit model; Strategic sampling scheme;

    References

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    1. 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.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, October.
    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. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    5. 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.
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    Cited by:
    1. Guevara, C. Angelo & Ben-Akiva, Moshe E., 2013. "Sampling of alternatives in Logit Mixture models," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 185-198.

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