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An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model

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  • Joel L. Horowitz

    (U.S. Environmental Protection Agency, Washington, D.C.)

  • Jürg M. Sparmann

    (University of California, Berkeley, California)

  • Carlos F. Daganzo

    (University of California, Berkeley, California)

Abstract

The Clark approximation, in which the maximum of two normally distributed random variables is approximated by a third normally distributed random variable, forms the basis of a relatively inexpensive technique for evaluating the choice probabilities of multinomial probit models. This paper reports the results of a series of numerical experiments in which the accuracy of probit computations based on the Clark approximation was investigated. In contrast to previous investigations, these experiments dealt with the accuracy of the results obtained when the Clark approximation is used for econometric estimation of the values of probit models' parameters and for prediction of choice probabilities using the estimated parameter values. It was found that the accuracy of the results obtained with the Clark approximation varies greatly from model to model. In many of the experiments the approximation performed quite satisfactorily, but in others it produced errors that probably would be causes for concern in practical work. It is difficult or impossible to judge the accuracy of results obtained using the Clark approximation without knowledge of the results that would be obtained using a computational technique that is known to be accurate. Consequently, in practical empirical work it often will not be possible to obtain reliable indicators of the Clark approximation's accuracy. However, it is likely that the errors resulting from use of the Clark approximation to estimate a probit model are small compared to the errors that would result from using the simpler logit model in a situation where the correct model specification is probit

Suggested Citation

  • Joel L. Horowitz & Jürg M. Sparmann & Carlos F. Daganzo, 1982. "An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model," Transportation Science, INFORMS, vol. 16(3), pages 382-401, August.
  • Handle: RePEc:inm:ortrsc:v:16:y:1982:i:3:p:382-401
    DOI: 10.1287/trsc.16.3.382
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    Cited by:

    1. Paul Gertler & Roland Sturm & Bruce Davidson, 1994. "Information and the Demand for Supplemental Medicare Insurance," NBER Working Papers 4700, National Bureau of Economic Research, Inc.
    2. Yai, Tetsuo & Iwakura, Seiji & Morichi, Shigeru, 1997. "Multinomial probit with structured covariance for route choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 195-207, June.
    3. 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.
    4. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.
    5. Deng, Wen & Lei, Hao & Zhou, Xuesong, 2013. "Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 132-157.
    6. Wada, Kentaro & Usui, Kento & Takigawa, Tsubasa & Kuwahara, Masao, 2018. "An optimization modeling of coordinated traffic signal control based on the variational theory and its stochastic extension," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 907-925.
    7. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    8. Tasos Nikoleris & Mark Hansen, 2012. "Queueing Models for Trajectory-Based Aircraft Operations," Transportation Science, INFORMS, vol. 46(4), pages 501-511, November.
    9. Sean F. Reardon & Benjamin R. Shear & Katherine E. Castellano & Andrew D. Ho, 2017. "Using Heteroskedastic Ordered Probit Models to Recover Moments of Continuous Test Score Distributions From Coarsened Data," Journal of Educational and Behavioral Statistics, , vol. 42(1), pages 3-45, February.
    10. 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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