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Sampling of alternatives in Logit Mixture models

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  • Guevara, C. Angelo
  • Ben-Akiva, Moshe E.

Abstract

Employing a strategy of sampling of alternatives is necessary for various transportation models that have to deal with large choice-sets. In this article, we propose a method to obtain consistent, asymptotically normal and relatively efficient estimators for Logit Mixture models while sampling alternatives. Our method is an extension of previous results for Logit and MEV models. We show that the practical application of the proposed method for Logit Mixture can result in a Naïve approach, in which the kernel is replaced by the usual sampling correction for Logit. We give theoretical support for previous applications of the Naïve approach, showing not only that it yields consistent estimators, but also providing its asymptotic distribution for proper hypothesis testing. We illustrate the proposed method using Monte Carlo experimentation and real data. Results provide further evidence that the Naïve approach is suitable and practical. The article concludes by summarizing the findings of this research, assessing their potential impact, and suggesting extensions of the research in this area.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:58:y:2013:i:c:p:185-198
    DOI: 10.1016/j.trb.2013.08.011
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    References listed on IDEAS

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    1. Chiou, Lesley & Walker, Joan L., 2007. "Masking identification of discrete choice models under simulation methods," Journal of Econometrics, Elsevier, vol. 141(2), pages 683-703, December.
    2. 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.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    4. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    5. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
    6. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    7. R. F. Engle & D. McFadden (ed.), 1986. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 4, number 4.
    8. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    9. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    10. 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.
    11. Cristian Angelo Guevara & Moshe E. Ben-Akiva, 2012. "Change of Scale and Forecasting with the Control-Function Method in Logit Models," Transportation Science, INFORMS, vol. 46(3), pages 425-437, August.
    12. 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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