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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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Bibliographic Info

Paper provided by Department of Economics, Institute for Business and Economic Research, UC Berkeley in its series Department of Economics, Working Paper Series with number qt94h8x4gd.

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Date of creation: 01 Jun 1995
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Handle: RePEc:cdl:econwp:qt94h8x4gd

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Keywords: Probit; Simulation; Social and Behavioral Sciences;

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References

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  1. Vassilis A. Hajivassiliou & Daniel L. McFadden & Paul Ruud, 1993. "Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives: Theoretical and Computational Results," Working Papers _024, Yale University.
  2. 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.
  3. 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.
  4. 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.
  5. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
  6. Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
  7. 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.
  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, 1999. "Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles," University of California Transportation Center, Working Papers qt45f996hh, University of California Transportation Center.
  2. 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.
  3. Eric Weese, 2011. "Political Mergers as Coalition Formation," Working Papers 997, Economic Growth Center, Yale University.
  4. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt3tb6j874, University of California Transportation Center.
  5. 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.
  6. Brownstone, David, 2001. "Discrete Choice Modeling for Transportation," University of California Transportation Center, Working Papers qt29v7d1pk, University of California Transportation Center.

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