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A practical technique to estimate multinomial probit models in transportation

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  • Bolduc, Denis

Abstract

The Multinomial Probit (MNP) formulation provides a very general framework to allow for inter-dependent alternatives in discrete choice analysis. Up until recently, its use was rather limited, mainly because of the computational difficulties associated with the evaluation of the choice probabilities which are multidimensional normal integrals. In recent years, the econometric estimation of Multinomial Probit models has greatly been focused on. Alternative simulation based approaches have been suggested and compared. Most approaches exploit a conventional estimation technique where easy to compute simulators replace the choice probabilities. For situations such as in transportation demand modelling where samples and choice sets are large, the existing literature clearly suggests the use of a maximum simulated likelihood (MSL) framework combined with a Geweke-Hajivassiliou-Keane (GHK) choice probability simulator. The present paper gives the computational details regarding the implementation of this practical estimation approach where the scores are computed analytically. This represents a contribution of the paper, because usually, numerical derivatives are used. The approach is tested on a 9-mode transportation choice model estimated with disaggregate data from Santiago, Chile. La formulation probit polytomique (MNP) permet d'analyser et de décrire de façon très flexible, le choix d'un individu parmi un ensemble de modalités inter-dépendantes. Les nombreux progrès effectués au cours des dernières années concernant l'estimation économétrique des modèles MNP, permet maintenant de contourner la problématique liée à l'évaluation d'intégrales normales multiples qui définissent les probabilités de sélection des modalités. Les diverses approches considérées exploitent généralement des simulateurs efficaces agissant comme substituts aux probabilités exactes de choix. Le simulateur ayant la faveur générale est le GHK, suggéré de façon indépendante par Geweke, Hajivassiliou et Keane. Pour les situations telles que généralement rencontrées dans le domaine des transports où les échantillons ainsi que les ensembles de choix sont de grande taille, la littérature suggère très clairement l'emploi d'une approche du maximum de vraisemblance utilisant le simulateur GHK pour approcher les probabilités de choix. Le présent article fournit les détails relatifs à l'utilisation de cette méthodologie dans un cadre du maximum de vraisemblance avec dériv ées analytiques. L'approche est ensuite testée sur un ensemble de données décrivant le choix entre neuf modes servant à relier le centre-ville de Santiago à des régions en périphérie.

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Bibliographic Info

Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 33 (1999)
Issue (Month): 1 (February)
Pages: 63-79

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Handle: RePEc:eee:transb:v:33:y:1999:i:1:p:63-79

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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. Ben-Akiva, M. & Bolduc, D. & Bradley, M., 1993. "Estimation of Travel Choice Models with Randomly Distributed Values of Time," Papers 9303, Laval - Recherche en Energie.
  3. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
  4. Gaudry, Marc J. I. & Jara-Diaz, Sergio R. & Ortuzar, Juan de Dios, 1989. "Value of time sensitivity to model specification," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 151-158, April.
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