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A general and operational representation of Generalised Extreme Value models

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  • Daly, Andrew
  • Bierlaire, Michel
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    Abstract

    Generalised 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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 40 (2006)
    Issue (Month): 4 (May)
    Pages: 285-305

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    Handle: RePEc:eee:transb:v:40:y:2006:i:4:p:285-305

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    1. 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.
    2. Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
    3. 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.
    4. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-24, March.
    5. Daly, Andrew, 1987. "Estimating "tree" logit models," Transportation Research Part B: Methodological, Elsevier, vol. 21(4), pages 251-267, August.
    6. 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.
    7. Ben-Akiva, Moshe & McFadden, Daniel & Train, Kenneth & Börsch-Supan, Axel, 2002. "Hybrid Choice Models: Progress and Challenges," Sonderforschungsbereich 504 Publications 02-29, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    8. 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.
    9. 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.
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    Cited by:
    1. Newman, Jeffrey P., 2008. "Normalization of network generalized extreme value models," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 958-969, December.
    2. 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.
    3. 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.
    4. 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.
    5. Laurie Garrow & Tudor Bodea & Misuk Lee, 2010. "Generation of synthetic datasets for discrete choice analysis," Transportation, Springer, vol. 37(2), pages 183-202, March.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Melo, Emerson, 2012. "A representative consumer theorem for discrete choice models in networked markets," Economics Letters, Elsevier, vol. 117(3), pages 862-865.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.

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