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Strategic sampling for large choice sets in estimation and application

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

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transa:v:46:y:2012:i:3:p:602-613
    DOI: 10.1016/j.tra.2011.11.004
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    References listed on IDEAS

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    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    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. 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.
    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. H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
    6. 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.
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    Cited by:

    1. Clifton, Kelly J. & Singleton, Patrick A. & Muhs, Christopher D. & Schneider, Robert J., 2016. "Development of destination choice models for pedestrian travel," Transportation Research Part A: Policy and Practice, Elsevier, vol. 94(C), pages 255-265.
    2. 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.
    3. Bart Capéau & André Decoster & Gijs Dekkers, 2016. "Estimating and Simulating with a Random Utility Random Opportunity Model of Job Choice Presentation and Application to Belgium," International Journal of Microsimulation, International Microsimulation Association, vol. 9(2), pages 144-191.

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