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Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters

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  • Liu, Yu-Hsin
  • Mahmassani, Hani S.

Abstract

This paper presents a procedure, named GAMNP, incorporating genetic algorithms (GAs) and nonlinear programming (NLP) techniques to find the "global" maximum likelihood estimate (MLE) in multinomial probit (MNP) model estimation. The GAMNP estimation procedure uses GAs to search for "good" starting points systematically and globally through the possible solution areas that satisfy the property of positive definite variance-covariance matrix; the NLP algorithm is then used to fine-tune the solutions obtained from the GAs procedure. A numerical experiment was conducted to test the performance of the GAMNP estimation procedure based on an artificial data set with known parameter values, model specification, and error structure. The log-likelihood function value, parameter accuracy measures, and the CPU execution time were adopted as performance measures in this experiment. The experimental results indicated that the GAMNP estimation procedure is able to find the global MLE in MNP model estimation when the analyst does not have a priori expectations of the magnitudes of the parameters. The highlight, the importance of using systematic starting solution search procedures, like those used in genetic algorithms, instead of selecting starting solutions arbitrarily.

Suggested Citation

  • Liu, Yu-Hsin & Mahmassani, Hani S., 2000. "Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 419-449, June.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:5:p:419-449
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    References listed on IDEAS

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    1. Charles E. Clark, 1961. "The Greatest of a Finite Set of Random Variables," Operations Research, INFORMS, vol. 9(2), pages 145-162, April.
    2. Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
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    Cited by:

    1. Karthik K. Srinivasan & Hani S. Mahmassani, 2005. "A Dynamic Kernel Logit Model for the Analysis of Longitudinal Discrete Choice Data: Properties and Computational Assessment," Transportation Science, INFORMS, vol. 39(2), pages 160-181, May.
    2. Batram, Manuel & Bauer, Dietmar, 2019. "On consistency of the MACML approach to discrete choice modelling," Journal of choice modelling, Elsevier, vol. 30(C), pages 1-16.
    3. Liu, Yu-Hsin, 2011. "Incorporating scatter search and threshold accepting in finding maximum likelihood estimates for the multinomial probit model," European Journal of Operational Research, Elsevier, vol. 211(1), pages 130-138, May.
    4. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    5. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    6. Rong-Chang Jou & David A. Hensher & Yu-Hsin Liu & Ching-Shu Chiu, 2010. "Urban Commuters’ Mode-switching Behaviour in Taipai, with an Application of the Bounded Rationality Principle," Urban Studies, Urban Studies Journal Limited, vol. 47(3), pages 650-665, March.
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    8. Jou, Rong-Chang & Lam, Soi-Hoi & Liu, Yu-Hsin & Chen, Ke-Hong, 2005. "Route switching behavior on freeways with the provision of different types of real-time traffic information," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(5), pages 445-461, June.
    9. Moonsoo Ko & Taewan Kim & Keemin Sohn, 2013. "Calibrating a social-force-based pedestrian walking model based on maximum likelihood estimation," Transportation, Springer, vol. 40(1), pages 91-107, January.
    10. Beeramoole, Prithvi Bhat & Arteaga, Cristian & Pinz, Alban & Haque, Md Mazharul & Paz, Alexander, 2023. "Extensive hypothesis testing for estimation of mixed-Logit models," Journal of choice modelling, Elsevier, vol. 47(C).

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