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The Estimation of Multinomial Probit Models: A New Calibration Algorithm

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  • Wagner A. Kamakura

    (Vanderbilt University, Nashville, Tennessee 37203)

Abstract

This study proposes the estimation of Multinomial Probit models using Mendell-Elston's approximation to the cumulative multivariate normal for the computation of choice probabilities. The accuracy of this numerical approximation in computing probabilities is compared with other procedures used in existing calibration programs. Finally, the proposed estimation procedure is tested on simulated choice data.

Suggested Citation

  • Wagner A. Kamakura, 1989. "The Estimation of Multinomial Probit Models: A New Calibration Algorithm," Transportation Science, INFORMS, vol. 23(4), pages 253-265, November.
  • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:4:p:253-265
    DOI: 10.1287/trsc.23.4.253
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    Citations

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    Cited by:

    1. DeSarbo, Wayne S. & Kim, Youngchan & Wedel, Michel & Fong, Duncan K. H., 1998. "A Bayesian approach to the spatial representation of market structure from consumer choice data," European Journal of Operational Research, Elsevier, vol. 111(2), pages 285-305, December.
    2. Haaijer, Marinus E., 1996. "Predictions in conjoint choice experiments : the x-factor probit model," Research Report 96B22, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    3. Zou, Yiyuan & Zhang, Honghai & Zhong, Gang & Liu, Hao & Feng, Dikun, 2021. "Collision probability estimation for small unmanned aircraft systems," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    4. Batram, Manuel & Bauer, Dietmar, 2019. "On consistency of the MACML approach to discrete choice modelling," Journal of choice modelling, Elsevier, vol. 30(C), pages 1-16.
    5. Kenetsu Uchida & Agachai Sumalee & David Watling & Richard Connors, 2007. "A Study on Network Design Problems for Multi-modal Networks by Probit-based Stochastic User Equilibrium," Networks and Spatial Economics, Springer, vol. 7(3), pages 213-240, September.
    6. Rinus Haaijer & Michel Wedel & Marco Vriens & Tom Wansbeek, 1998. "Utility Covariances and Context Effects in Conjoint MNP Models," Marketing Science, INFORMS, vol. 17(3), pages 236-252.
    7. Sumalee, Agachai & Tan, Zhijia & Lam, William H.K., 2009. "Dynamic stochastic transit assignment with explicit seat allocation model," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 895-912, September.
    8. Martinetti, Davide & Geniaux, Ghislain, 2017. "Approximate likelihood estimation of spatial probit models," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 30-45.
    9. repec:dgr:rugsom:96b22 is not listed on IDEAS
    10. Bhat, Chandra R., 2018. "New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 238-256.
    11. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.

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