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

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  • Kenneth E. Train.

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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Bibliographic Info

Paper provided by University of California at Berkeley in its series Economics Working Papers with number 95-237.

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Date of creation: 01 Jun 1995
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Handle: RePEc:ucb:calbwp:95-237

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References

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  1. Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990. "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Cowles Foundation Discussion Papers 960, Cowles Foundation for Research in Economics, Yale University.
  2. Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
  3. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-52, July.
  5. 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.
  6. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
  7. 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.
  8. 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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Citations

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Cited by:
  1. 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.
  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. 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.
  4. Brownstone, David, 2001. "Discrete Choice Modeling for Transportation," University of California Transportation Center, Working Papers qt29v7d1pk, University of California Transportation Center.
  5. 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.
  6. Eric Weese, 2011. "Political Mergers as Coalition Formation," Working Papers 997, Economic Growth Center, Yale University.

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