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

The authors 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. The authors consider popular RQMC constructions such as randomized Sobol', Faure, and Halton points, but the main emphasis is on randomly-shifted lattice rules, for which the authors study how to select the parameters as a function of the considered class of integrands. The authors 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 the 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 the examples, the performance of all RQMC methods degrades rapidly when we simultaneously increase the dimension and the number of observations per individual.

• Record URL:
  • http://www.sciencedirect.com/science/article/pii/S0191261511001457
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier.
• Authors:
  • Munger, D
  • L'Ecuyer, P
  • Bastin, F
  • Cirillo, C
  • Tuffin, B
• Publication Date: 2012-2

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References; Tables;
• Pagination: pp 305-320
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 46
  • Issue Number: 2
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Choice models; Discrete systems; Lattices (Mathematics); Logits; Monte Carlo method; Travel behavior
• Subject Areas: Planning and Forecasting; Transportation (General); I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 01366017
• Record Type: Publication
• Files: TRIS
• Created Date: Mar 23 2012 8:45AM