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

Content Provider	Semantic Scholar
Author	Munger, D. L'Ecuyer, Pierre Bastin, Fabian Cirillo, Cinzia Tuffin, Bruno
Copyright Year	2010
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.
Starting Page	305
Ending Page	320
Page Count	16
File Format	PDF HTM / HTML
DOI	10.1016/j.trb.2011.10.005
Alternate Webpage(s)	http://www.iro.umontreal.ca/~lecuyer/myftp/papers/mlogit-rqmc-app.pdf
Alternate Webpage(s)	https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2010-47.pdf
Alternate Webpage(s)	https://cinziacirillo.weebly.com/uploads/5/3/6/0/53607733/trb2012.pdf
Alternate Webpage(s)	http://www.iro.umontreal.ca/~lecuyer/myftp/papers/mlogit-rqmc.pdf
Alternate Webpage(s)	http://www.iro.umontreal.ca/~lecuyer/myftp/papers/iatbr-CIRRELT-2010-47.pdf
Alternate Webpage(s)	https://doi.org/10.1016/j.trb.2011.10.005
Volume Number	46
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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