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

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  • Kenneth 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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Paper provided by University of California at Berkeley, Econometrics Laboratory Software Archive in its series Working Papers with number _009.

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Handle: RePEc:wop:calbem:_009

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  1. 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 403-26, March.
  2. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
  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 & Paul Ruud, 1993. "Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives: Theoretical and Computational Results," Working Papers _024, Yale University.
  5. V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series /1997/328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. 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.
  7. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
  8. Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
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Cited by:
  1. 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.
  2. Brownston, 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 qt7rf7s3nx, University of California Transportation Center.
  3. 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.
  4. 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.
  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.

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