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Application of an adaptive Monte Carlo algorithm to mixed logit estimation

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  • Bastin, Fabian
  • Cirillo, Cinzia
  • Toint, Philippe L.

Abstract

This paper presents the application of a new algorithm for maximizing the simulated likelihood functions appearing in the estimation of mixed multinomial logit (MMNL) models. The method uses Monte Carlo sampling to produce the approximate likelihood function and dynamically adapts the number of draws on the basis of statistical estimators of the simulation error and simulation bias. Its convergence from distant starting points is ensured by a trust-region technique, in which improvement is ensured by locally maximizing a quadratic model of the objective function. Simulated data are first used to assess the quality of the results obtained and the relative performance of several algorithmic variants. These variants involve, in particular, different techniques for approximating the model's Hessian and the substitution of the trust-region mechanism by a linesearch. The algorithm is also applied to a real case study arising in the context of a recent Belgian transportation model. The performance of the new Monte Carlo algorithm is shown to be competitive with that of existing tools using low discrepancy sequences.

Suggested Citation

  • Bastin, Fabian & Cirillo, Cinzia & Toint, Philippe L., 2006. "Application of an adaptive Monte Carlo algorithm to mixed logit estimation," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 577-593, August.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:7:p:577-593
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    Cited by:

    1. Cinzia Cirillo & Renting Xu & Fabian Bastin, 2016. "A Dynamic Formulation for Car Ownership Modeling," Transportation Science, INFORMS, vol. 50(1), pages 322-335, February.
    2. Carolina Osorio & Michel Bierlaire, 2013. "A Simulation-Based Optimization Framework for Urban Transportation Problems," Operations Research, INFORMS, vol. 61(6), pages 1333-1345, December.
    3. Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    4. Akar, Gulsah & Clifton, Kelly J. & Doherty, Sean T., 2012. "Redefining activity types: Who participates in which leisure activity?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1194-1204.
    5. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    6. Cinzia Cirillo & Kay Axhausen, 2010. "Dynamic model of activity-type choice and scheduling," Transportation, Springer, vol. 37(1), pages 15-38, January.
    7. Stefania Bellavia & Nataša Krejić & Benedetta Morini, 2020. "Inexact restoration with subsampled trust-region methods for finite-sum minimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 701-736, July.
    8. Bliemer, Michiel C.J. & Rose, John M., 2011. "Experimental design influences on stated choice outputs: An empirical study in air travel choice," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(1), pages 63-79, January.
    9. Gulsah Akar & Kelly Clifton & Sean Doherty, 2011. "Discretionary activity location choice: in-home or out-of-home?," Transportation, Springer, vol. 38(1), pages 101-122, January.

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