Discrete choice analysis

Discrete choice analysis is a statistical technique. In these models the dependent variable is a binary variable. Instances of discrete choice analysis are probit, logit and multinomial models. They are applied in econometrics, marketing research and transportation mode and route choice.

= Specific model typesBen-Akiva, M. and S.R. Lerman (1985). Discrete Choice Analysis: Theory and Application to Travel Demand,Cambridge, MA: MIT Press.] Ben-Akiva, M. and M. Bierlaire (1999). “Discrete Choice Methods and Their Applications to Short TermTravel Decisions.” In R.W. Hall (ed.), Handbook of Transportation Science.] Bekhor, S., M. E. Ben-Akiva, et al. (2006). "Evaluation of choice set generation algorithms for route choice models." Annals of Operations Research 144(1): 235-247.] =

* Probit
* Logit
* Multinomial logit (MNL) - enhanced logit to allow for more than two alternatives in a choice
* Multinomial probit model

MNL is not suitable for problems with correlated alternatives due to the IIA property (irrelevance of independent alternatives). (See the blue bus/red bus example or path choice exampleA number of alternatives have been proposed to overcome this problem:

* Nested logit - captures correlations between alternatives by partitioning the choice set into 'nests'
* Cross-nested logit [Vovsha, P. (1997). “The Cross-Nested Logit Model: Application to Mode Choice in the Tel-Aviv Metropolitan Area.” Transportation Research Record, 1607, 6–15.] (CNL) - alternatives may belong to more than one nest

* Generalised extreme value model [McFadden, D. (1978). “Modeling the Choice of Residential Location.” In A. Karlqvist et al. (eds.), Spatial Interaction Theory and Residential Location, North Holland, Amsterdam pp. 75–96.] - the general class of model, derived from the random utility model to which multinomial logit and nested logit belong

* Mother logit
* Hierarchical logit

* C-logit [Cascetta, E., A. Nuzzolo, F. Russo, and A.Vitetta (1996). “A Modified Logit Route Choice Model OvercomingPath Overlapping Problems: Specification and Some Calibration Results for Interurban Networks.” In J.B.Lesort (ed.), Transportation and Traffic Theory. Proceedings from the Thirteenth International Symposiumon Transportation and Traffic Theory, Lyon, France, Pergamon pp. 697–711.] - captures correlations between alternatives using with a 'commonality factor'

* Path size logit

* Paired combinatorial logit [Chu, C. (1989). “A Paired Combinatorial Logit Model for Travel Demand Analysis.” In Proceedings of the 5th World Conference on Transportation Research, 4, Ventura, CA, pp. 295–309.]

* Hybrid or mixed logit model - multinomial probit model with logit kernel, [McFadden, D. and K. Train (2000). “Mixed MNL Models for Discrete Response.” Journal of Applied Econometrics,15(5), 447–470.] [Ben-Akiva, M. and D. Bolduc (1996). “Multinomial Probit with a Logit Kernel and a General Parametric Specification of the Covariance Structure.” Working Paper, 1996.] . Can be applied to route choice [Bekhor, S., Ben-Akiva, and M.S. Ramming (2002). “Adaptation of Logit Kernel to Route Choice Situation.”Transportation Research Record, 1805, 78–85.]

* Latent class choice models

Also see:
* full review of models for route choice [Ramming, M.S. (2001). “Network Knowledge and Route Choice.” Unpublished Ph.D. Thesis, Massachusetts Institute of Technology. MIT catalogue: http://library.mit.edu/item/001107149]

= Choice set generation methods for route choice problems =

* k-shortest routes, with link elimination and link penalty
* Labelling
* Simulation

References