IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v40y2006i7p577-593.html
   My bibliography  Save this article

Application of an adaptive Monte Carlo algorithm to mixed logit estimation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(05)00102-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    2. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    4. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
    5. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    6. Elias L. Khalil (ed.), 2003. "Trust," Books, Edward Elgar Publishing, number 2482.
    7. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    8. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    2. Staus, Alexander, 2008. "Standard and Shuffled Halton Sequences in a Mixed Logit Model," Working Papers 93856, Universitaet Hohenheim, Institute of Agricultural Policy and Agricultural Markets.
    3. Sarrias, Mauricio, 2016. "Discrete Choice Models with Random Parameters in R: The Rchoice Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i10).
    4. Bliemer, Michiel C.J. & Rose, John M., 2010. "Construction of experimental designs for mixed logit models allowing for correlation across choice observations," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 720-734, July.
    5. Marco A. Palma & Dmitry V. Vedenov & David Bessler, 2020. "The order of variables, simulation noise, and accuracy of mixed logit estimates," Empirical Economics, Springer, vol. 58(5), pages 2049-2083, May.
    6. Yu, Jie & Goos, Peter & Vandebroek, Martina, 2010. "Comparing different sampling schemes for approximating the integrals involved in the efficient design of stated choice experiments," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1268-1289, December.
    7. Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariat," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    8. Chiou, Lesley & Walker, Joan L., 2007. "Masking identification of discrete choice models under simulation methods," Journal of Econometrics, Elsevier, vol. 141(2), pages 683-703, December.
    9. Train, Kenneth & Wilson, Wesley W., 2008. "Estimation on stated-preference experiments constructed from revealed-preference choices," Transportation Research Part B: Methodological, Elsevier, vol. 42(3), pages 191-203, March.
    10. Czajkowski, Mikołaj & Budziński, Wiktor, 2019. "Simulation error in maximum likelihood estimation of discrete choice models," Journal of choice modelling, Elsevier, vol. 31(C), pages 73-85.
    11. Hess, Stephane, 2007. "Posterior analysis of random taste coefficients in air travel behaviour modelling," Journal of Air Transport Management, Elsevier, vol. 13(4), pages 203-212.
    12. Stephane Hess, 2014. "Latent class structures: taste heterogeneity and beyond," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 14, pages 311-330, Edward Elgar Publishing.
    13. Liu, Henry X. & He, Xiaozheng & Recker, Will, 2007. "Estimation of the time-dependency of values of travel time and its reliability from loop detector data," Transportation Research Part B: Methodological, Elsevier, vol. 41(4), pages 448-461, May.
    14. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    15. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    16. Faulques, Martin & Bonnet, Jean & Bourdin, Sébastien & Juge, Marine & Pigeon, Jonas & Richard, Charlotte, 2022. "Generational effect and territorial distributive justice, the two main drivers for willingness to pay for renewable energies," Energy Policy, Elsevier, vol. 168(C).
    17. Martínez-Pardo, Ana & Orro, Alfonso & Garcia-Alonso, Lorena, 2020. "Analysis of port choice: A methodological proposal adjusted with public data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 178-193.
    18. Falco, Paolo & Maloney, William F. & Rijkers, Bob & Sarrias, Mauricio, 2015. "Heterogeneity in subjective wellbeing: An application to occupational allocation in Africa," Journal of Economic Behavior & Organization, Elsevier, vol. 111(C), pages 137-153.
    19. Juan Carlos Martín & Concepción Román & Cira Mendoza, 2018. "Determinants for sun-and-beach self-catering accommodation selection," Tourism Economics, , vol. 24(3), pages 319-336, May.
    20. Isler, Cassiano Augusto & Blumenfeld, Marcelo & Caldeira, Gabriel Pereira & Roberts, Clive, 2024. "Long-Distance railway mode choice in Brazil: Evidence from a discrete choice experiment," Research in Transportation Economics, Elsevier, vol. 104(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:40:y:2006:i:7:p:577-593. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.