A general and operational representation of Generalised Extreme Value models
AbstractGeneralised extreme value models provide an interesting theoretical framework to develop closed-form random utility models. Unfortunately, few instances of this family are to be found as operational models in practice. The form of the model, based on a generating function G which must satisfy specific properties, is rather complicated. Fundamentally, it is not an easy task to translate an intuitive perception of the correlation structure by the modeller into a concrete G function. And even if the modeller succeeds in proposing a new G function, the task of proving that it indeed satisfies the properties is cumbersome. In modelling transportation demand, researchers face the problem that many of the choices they wish to model interact in complex ways. One approach to this problem is to use mixed logit models, exploiting the power of simulation-based estimation, to incorporate the interactions required. An alternative approach, however, which is followed in this paper, is to exploit further the GEV model family originally proposed by McFadden [McFadden, D., 1978. Modelling the choice of residential location. In: Karlquist, A. et al. (Eds.), Spatial Interaction Theory and Residential Location. North-Holland, Amsterdam, pp. 75-96]. The main objectives of this paper are (i) to provide a general theoretical foundation, so that the development of new GEV models will be easier in the future, and (ii) to propose an easy way of generating new GEV models without a need for complicated proofs. Our technique requires only a network structure capturing the underlying correlation of the choice situation under consideration. If the network complies with some simple conditions, we show how to build an associated model. We prove that it is indeed a GEV model and, therefore, complies with random utility theory. The multinomial logit, the nested logit and the cross-nested logit models are specific instances of our class of models. So are the recent GenL model, combining choice set generation and choice model and some specialised compound models used in recent transportation work. Probability, expected maximum utility and elasticity formulae for the class of models are provided.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Transportation Research Part B: Methodological.
Volume (Year): 40 (2006)
Issue (Month): 4 (May)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Daly, Andrew, 1987. "Estimating "tree" logit models," Transportation Research Part B: Methodological, Elsevier, vol. 21(4), pages 251-267, August.
- Bhat, Chandra R., 1998. "Analysis of travel mode and departure time choice for urban shopping trips," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 361-371, August.
- Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
- Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
- Axel Börsch-Supan & Moshe Ben-Akiva & Kenneth Train & Daniel McFadden, 2002.
"Hybrid Choice Models: Progress and Challenges,"
MEA discussion paper series
02009, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
- Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
- Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-24, March.
- Daly, Andrew, 2001. "Alternative tree logit models: comments on a paper of Koppelman and Wen," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 717-724, September.
- Swait, Joffre, 2001. "Choice set generation within the generalized extreme value family of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 643-666, August.
- Vega, Amaya & Reynolds-Feighan, Aisling, 2009. "A methodological framework for the study of residential location and travel-to-work mode choice under central and suburban employment destination patterns," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(4), pages 401-419, May.
- Pinjari, Abdul Rawoof, 2011. "Generalized extreme value (GEV)-based error structures for multiple discrete-continuous choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 474-489, March.
- Melo, Emerson, 2012. "A representative consumer theorem for discrete choice models in networked markets," Economics Letters, Elsevier, vol. 117(3), pages 862-865.
- Meng, Qiang & Liu, Zhiyuan & Wang, Shuaian, 2012. "Optimal distance tolls under congestion pricing and continuously distributed value of time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(5), pages 937-957.
- Bierlaire, M. & Bolduc, D. & McFadden, D., 2008. "The estimation of generalized extreme value models from choice-based samples," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 381-394, May.
- Fosgerau, M. & Bierlaire, M., 2009. "Discrete choice models with multiplicative error terms," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 494-505, June.
- Chorus, Caspar G. & Arentze, Theo A. & Timmermans, Harry J.P., 2008. "A Random Regret-Minimization model of travel choice," Transportation Research Part B: Methodological, Elsevier, vol. 42(1), pages 1-18, January.
- Chorus, Caspar G. & Timmermans, Harry J.P., 2009. "Measuring user benefits of changes in the transport system when traveler awareness is limited," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(5), pages 536-547, June.
- Marzano, Vittorio & Papola, Andrea, 2008. "On the covariance structure of the Cross-Nested Logit model," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 83-98, February.
- Peter Davis & Pasquale Schiraldi, 2013. "The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products," LSE Research Online Documents on Economics 54252, London School of Economics and Political Science, LSE Library.
- Marzano, Vittorio & Papola, Andrea & Simonelli, Fulvio & Vitillo, Roberta, 2013. "A practically tractable expression of the covariances of the Cross-Nested Logit model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 1-11.
- Laurie Garrow & Tudor Bodea & Misuk Lee, 2010. "Generation of synthetic datasets for discrete choice analysis," Transportation, Springer, vol. 37(2), pages 183-202, March.
- Adriaan Hendrik van der Weijde & Vincent A.C. van den Berg, 2013. "Stochastic User Equilibrium Traffic Assignment with Price-sensitive Demand: Do Methods matter (much)?," Tinbergen Institute Discussion Papers 13-209/VIII, Tinbergen Institute.
- Bekhor, Shlomo & Prashker, Joseph N., 2008. "GEV-based destination choice models that account for unobserved similarities among alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 42(3), pages 243-262, March.
- Newman, Jeffrey P., 2008. "Normalization of network generalized extreme value models," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 958-969, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.