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Estimation des Modeles Probit Polytomiques: Un Survol des Techniques

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  • Bolduc, D.
  • Kaci, M.

Abstract

The Multinomial Probit (MNP) model provides the most general framework to allow for interdependent alternatives in discrete choice analysis. The primary impediment to this methodology is related to the dimensionality of the response probabilities which are multifold normal integrals of about the size of the choice set. During the last two decades, numerous researches have been devoted to develop practical methodologies to replace these hard to compute choice probabilities in the estimation process. The main objective of this paper is to survey the major and the most important of these techniques. Parce qu’il admet des structures très générales d’interdépendance entre les modalités, le probit polytomique (MNP) fournit une des formes les plus intéressantes pour modéliser les choix discrets qui découlent d’une maximisation d’utilité aléatoire. L’obstacle majeur et bien connu dans l’estimation de ce type de modèle tient à la complexité que prennent les calculs lorsque le nombre de modalités considérées est élevé. Cette situation est due essentiellement à la présence d’intégrales normales multidimensionnelles qui définissent les probabilités de sélection. Au cours des deux dernières décennies, de nombreux efforts ont été effectués visant à produire des méthodes qui permettent de contourner les difficultés de calcul liées à l’estimation des modèles probit polytomiques. L’objectif de ce texte consiste à produire un survol critique des principales méthodes mises de l’avant jusqu’à maintenant pour rendre opérationnel le cadre MNP. Nous espérons qu’il éclairera les praticiens de ces modèles quant au choix de technique d’estimation à favoriser au cours des prochaines années.

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Bibliographic Info

Paper provided by Laval - Recherche en Energie in its series Papers with number 9127.

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Length: 33 pages
Date of creation: 1991
Date of revision:
Handle: RePEc:fth:lavaen:9127

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Phone: (418) 656-2096
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Web page: http://www.green.ecn.ulaval.ca/
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Keywords: econometrics ; economic models;

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References

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  1. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  2. 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.
  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. Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff & John N. Morris, 1990. "Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," NBER Working Papers 3343, National Bureau of Economic Research, Inc.
  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. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-64, May.
  7. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
  8. Christian GOURIEROUX & Alain MONFORT, 1991. "Simulation Based Inference in Models with Heterogeneity," Annales d'Economie et de Statistique, ENSAE, issue 20-21, pages 69-107.
  9. 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.
  10. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
  11. Ben-Akiva, M. & Bolduc, D., 1991. "Multinomial Probit with Autoregressive Error Structure," Papers 9123, Laval - Recherche en Energie.
  12. Berkovec, James & Stern, Steven, 1991. "Job Exit Behavior of Older Men," Econometrica, Econometric Society, vol. 59(1), pages 189-210, January.
  13. Bolduc, D. & Kaci, M., 1991. "Multinomial Probit Models with Factor-Based Autoregressive Errors: A Computationally Efficient Estimation Approach," Papers 9118, Laval - Recherche en Energie.
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Cited by:
  1. Mohamed Goaïed & Samir Ghazouani, 1993. "Analyse micro-économétrique de la demande de transport urbain pour la ville de Tunis," Économie et Prévision, Programme National Persée, vol. 108(2), pages 47-62.

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