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Estimation of the mixed logit likelihood function by randomized quasi-Monte Carlo

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  • Munger, D.
  • L’Ecuyer, P.
  • Bastin, F.
  • Cirillo, C.
  • Tuffin, B.

Abstract

We examine the effectiveness of randomized quasi-Monte Carlo (RQMC) techniques to estimate the integrals that express the discrete choice probabilities in a mixed logit model, for which no closed form formula is available. These models are used extensively in travel behavior research. We consider popular RQMC constructions such as randomized Sobol’, Faure, and Halton points, but our main emphasis is on randomly-shifted lattice rules, for which we study how to select the parameters as a function of the considered class of integrands. We compare the effectiveness of all these methods and of standard Monte Carlo (MC) to reduce both the variance and the bias when estimating the log-likelihood function at a given parameter value. In our numerical experiments, randomized lattice rules (with carefully selected parameters) and digital nets are the best performers and they reduce the bias as much as the variance. With panel data, in our examples, the performance of all RQMC methods degrades rapidly when we simultaneously increase the dimension and the number of observations per individual.

Suggested Citation

  • Munger, D. & L’Ecuyer, P. & Bastin, F. & Cirillo, C. & Tuffin, B., 2012. "Estimation of the mixed logit likelihood function by randomized quasi-Monte Carlo," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 305-320.
    • Handle: RePEc:eee:transb:v:46:y:2012:i:2:p:305-320
    DOI: 10.1016/j.trb.2011.10.005
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    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. Fabian Bastin & Cinzia Cirillo & Philippe L. Toint, 2010. "Estimating Nonparametric Random Utility Models with an Application to the Value of Time in Heterogeneous Populations," Transportation Science, INFORMS, vol. 44(4), pages 537-549, November.
    3. 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.
    4. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
    5. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    6. Fabian Bastin & Cinzia Cirillo & Philippe Toint, 2006. "An adaptive Monte Carlo algorithm for computing mixed logit estimators," Computational Management Science, Springer, vol. 3(1), pages 55-79, January.
    7. Cirillo, C. & Axhausen, K.W., 2006. "Evidence on the distribution of values of travel time savings from a six-week diary," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(5), pages 444-457, June.
    8. Brownstone, David & Bunch, David S. & Train, Kenneth, 2000. "Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 315-338, June.
    9. Hess, Stephane & Bierlaire, Michel & Polak, John W., 2005. "Estimation of value of travel-time savings using mixed logit models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 221-236.
    10. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    11. Pierre L’Ecuyer, 2009. "Quasi-Monte Carlo methods with applications in finance," Finance and Stochastics, Springer, vol. 13(3), pages 307-349, September.
    12. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    13. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    14. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    15. Brownston, David & Bunch, David S. & Train, Kenneth, 1999. "Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles," University of California Transportation Center, Working Papers qt7rf7s3nx, University of California Transportation Center.
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    7. Tien Mai & Fabian Bastin & Emma Frejinger, 2018. "A decomposition method for estimating recursive logit based route choice models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 253-275, September.

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