Abstract
Fosgerau et al. (2013) recently proposed the recursive logit (RL) model for route choice problems, that can be consistently estimated and easily used for prediction without any sampling of choice sets. Its estimation however requires solving many large-scale systems of linear equations, which can be computationally costly for real data sets. We design a decomposition (DeC) method in order to reduce the number of linear systems to be solved, opening the possibility to estimate more complex RL based models, for instance mixed RL models. We test the performance of the DeC method by estimating the RL model on two networks of more than 7000 and 40,000 links, and we show that the DeC method significantly reduces the estimation time. We also use the DeC method to estimate two mixed RL specifications, one using random coefficients and one incorporating error components associated with subnetworks (Frejinger and Bierlaire 2007). The models are estimated on a real network and a cross-validation study is performed. The results suggest that the mixed RL models can be estimated in a reasonable time with the DeC method. These models yield sensible parameter estimates and the in-sample and out-of sample fits are significantly better than the RL model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bastin F, Cirillo C, Toint PhL (2006) Convergence theory for nonconvex stochastic programming with an application to mixed logit. Math Program Ser B 108(2–3):207–234
Bekhor S, Ben-Akiva M, Ramming M (1805) Adaptation of logit kernel to route choice situation. Transp Res Record 78–85:2002
Ben-Akiva M, Bierlaire M (1999) Discrete choice methods and their applications to short-term travel decisions. In: Hall R (ed.) Handbook of Transportation Science, pp 5–34. Kluwer
Ben-Akiva M (1973) The structure of travel demand models. PhD thesis, MIT
Bolduc D, Ben-Akiva M (1991) A multinomial probit formulation for large choice sets. In: Proceedings of the 6th International Conference on Travel Behaviour, vol 2, pp 243–258
Broyden CG (1970) The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA J Appl Math 6(1):76–90
Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13(3):317–322
Fosgerau M, Frejinger E, Karlström A (2013) A link based network route choice model with unrestricted choice set. Transp Res Part B 56:70–80
Frejinger E, Bierlaire M, Ben-Akiva M (2009) Sampling of alternatives for route choice modeling. Transp Res Part B 43(10):984–994
Frejinger E, Bierlaire M (2007) Capturing correlation with subnetworks in route choice models. Transp Res Part B 41(3):363–378
Goldfarb D (1970) A family of variable metric updates derived by variational means. Math Comput 24(109):23–26
Lai X, Bierlaire M (2015) Specification of the cross nested logit model with sampling of alternatives for route choice models. Transp Res Part B 80:220–234
Mai T (2016) A method of integrating correlation structures for a generalized recursive route choice model. Transp Res Part B 93(1):146–161
Mai T, Fosgerau M, Frejinger E (2015a) A nested recursive logit model for route choice analysis. Transp Res Part B 75(1):100–112
Mai T, Frejinger E, Bastin F (2015b) A misspecification test for logit based route choice models. Econ Transp 4(4):215–226
McFadden D (1978) Modelling the choice of residential location. In: Karlqvist A, Lundqvist L, Snickars F, Weibull J (eds) Spatial Interaction Theory and Residential Location. North-Holland, Amsterdam, pp 75–96
McFadden DL, Train K (2000) Mixed MNL models for discrete response. J Appl Econ 15(5):447–470
Munger D, L’Ecuyer P, Bastin F, Cirillo C, Tuffin B (2012) Estimation of the mixed logit likelihood function by randomized quasi-monte carlo. Transp Res Part B 46(2):305–320
Nocedal J, Wright SJ (2006) Numer Optim, 2nd edn. Springer, New York, NY, USA
Rust J (1987) Optimal replacement of GMC bus engines: an empirical model of Harold Zurcher. Econometrica 55(5):999–1033
Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24(111):647–656
Train K (2003) Discrete choice methods with simulation. Cambridge University Press
Zimmermann M, Mai T, Frejinger E (2016) Bike route choice modeling using GPS data without choice sets of paths. CIRRELT-2016-49, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation
Acknowledgements
This research was funded by Natural Sciences and Engineering Research Council of Canada (NSERC), discovery grant 435678-2013. We have benefited from valuable discussions with Mogens Fosgerau. The paper has also been improved thanks to the comments of the three anonymous reviewers.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mai, T., Bastin, F. & Frejinger, E. A decomposition method for estimating recursive logit based route choice models . EURO J Transp Logist 7, 253–275 (2018). https://doi.org/10.1007/s13676-016-0102-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13676-016-0102-3