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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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    3. 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.
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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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