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Simulation Methods for Probit and Related Models Based on Convenient Error Partitioning

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  • Train, Kenneth E.

Abstract

Two probit simulators are described that are conceptually and computationally simple. The first is based on simulating the utilities of the non-chosen alternatives and calculating the probability that the chosen alternative's utility exceeds this maximum. This simulator is apparently new. The second, which is implicit in the discussions of McFadden (1989) and Bolduc (1992), is applicable when the covariance among utilities arises from random parameters and/or error components that are common across alternatives. The parameters and common error components are simulated, and then the probability that the observed event occurs is calculated conditional on these values. Both simulators are unbiased, strictly positive, and continuous. The second is twice-differentiable, while the first has points of non-differentiability. Both are easy to program and can be expected to be very fast computationa- lly.
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  • Train, Kenneth E., 1995. "Simulation Methods for Probit and Related Models Based on Convenient Error Partitioning," Department of Economics, Working Paper Series qt94h8x4gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    • Handle: RePEc:cdl:econwp:qt94h8x4gd
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    1. Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
    2. Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
    3. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    4. Carlos F. Daganzo & Fernando Bouthelier & Yosef Sheffi, 1977. "Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm," Transportation Science, INFORMS, vol. 11(4), pages 338-358, November.
    5. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-952, July.
    6. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    7. Charles E. Clark, 1961. "The Greatest of a Finite Set of Random Variables," Operations Research, INFORMS, vol. 9(2), pages 145-162, April.
    8. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
    9. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    10. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    2. Brownstone, David & Bunch, David S. & Train, Kenneth, 2000. "Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 315-338, June.
    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. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    5. Brownstone, David, 2001. "Discrete Choice Modeling for Transportation," University of California Transportation Center, Working Papers qt29v7d1pk, University of California Transportation Center.
    6. Eric Weese, 2011. "Political Mergers as Coalition Formation," Working Papers 997, Economic Growth Center, Yale University.
    7. Zhenshan Chen & Stephen K. Swallow & Ian T. Yue, 2020. "Non-participation and Heterogeneity in Stated: A Double Hurdle Latent Class Approach for Climate Change Adaptation Plans and Ecosystem Services," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(1), pages 35-67, September.
    8. Siros Tongchure, 2013. "Cassava Smallholders’ Participation in Contract Farming in Nakhon Ratchasrima Province, Thailand," Journal of Social and Development Sciences, AMH International, vol. 4(7), pages 332-338.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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