IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v144y2006i1p287-30010.1007-s10479-006-0015-x.html
   My bibliography  Save this article

A theoretical analysis of the cross-nested logit model

Author

Listed:
  • Michel Bierlaire

Abstract

The emergence of Intelligent Transportation Systems and the associated technologies has increased the need for complex models and algorithms. Namely, real-time information systems, directly influencing transportation demand, must be supported by detailed behavioral models capturing travel and driving decisions. Discrete choice models methodology provide an appropriate framework to capture such behavior. Recently, the Cross-Nested Logit (CNL) model has received quite a bit of attention in the literature to capture decisions such as mode choice, departure time choice and route choice. %The CNL model is an extension of the Nested Logit model, providing %more flexibility at the cost of some complexity in the model formulation. In this paper, we develop on the general formulation of the Cross Nested Logit model proposed by Ben-Akiva and Bierlaire (1999) and based on the Generalized Extreme Value (GEV) model. We show that it is equivalent to the formulations byby Papola (2004) and Wen and Koppelman (2001). We also show that the formulations by Small(1987) and Vovsha(1997) are special cases of this formulation. We formally prove that the Cross-Nested Logit model is indeed a member of the GEV models family. In doing so, we clearly distinguish between conditions that are necessary to prove consistency with the GEV theory, from normalization conditions. Finally, we propose to estimate the model with non-linear programming algorithms, instead of heuristics proposed in the literature. In order to make it operational, we provide the first derivatives of the log-likelihood function, which are necessary to such optimization procedures. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Michel Bierlaire, 2006. "A theoretical analysis of the cross-nested logit model," Annals of Operations Research, Springer, vol. 144(1), pages 287-300, April.
    • Handle: RePEc:spr:annopr:v:144:y:2006:i:1:p:287-300:10.1007/s10479-006-0015-x
    DOI: 10.1007/s10479-006-0015-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-0015-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-0015-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michel Bierlaire & Tsippy Lotan & Philippe Toint, 1997. "On The Overspecification of Multinomial and Nested Logit Models Due to Alternative Specific Constants," Transportation Science, INFORMS, vol. 31(4), pages 363-371, November.
    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. 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.
    4. Bhat, Chandra R., 1995. "A heteroscedastic extreme value model of intercity travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 471-483, December.
    5. Langche Zeng, 2000. "A Heteroscedastic Generalized Extreme Value Discrete Choice Model," Sociological Methods & Research, , vol. 29(1), pages 118-144, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abbe, E. & Bierlaire, M. & Toledo, T., 2007. "Normalization and correlation of cross-nested logit models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 795-808, August.
    2. Koppelman, Frank S. & Sethi, Vaneet, 2005. "Incorporating variance and covariance heterogeneity in the Generalized Nested Logit model: an application to modeling long distance travel choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 39(9), pages 825-853, November.
    3. Sasic, Ana & Habib, Khandker Nurul, 2013. "Modelling departure time choices by a Heteroskedastic Generalized Logit (Het-GenL) model: An investigation on home-based commuting trips in the Greater Toronto and Hamilton Area (GTHA)," Transportation Research Part A: Policy and Practice, Elsevier, vol. 50(C), pages 15-32.
    4. Mai, Tien, 2016. "A method of integrating correlation structures for a generalized recursive route choice model," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 146-161.
    5. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    6. Zhang, Junyi & Timmermans, Harry & Borgers, Aloys & Wang, Donggen, 2004. "Modeling traveler choice behavior using the concepts of relative utility and relative interest," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 215-234, March.
    7. Daly, Andrew & Bierlaire, Michel, 2006. "A general and operational representation of Generalised Extreme Value models," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 285-305, May.
    8. Wang, Hai & Yang, Hai, 2019. "Ridesourcing systems: A framework and review," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 122-155.
    9. Flügel, Stefan & Halse, Askill H. & Ortúzar, Juan de Dios & Rizzi, Luis I., 2015. "Methodological challenges in modelling the choice of mode for a new travel alternative using binary stated choice data – The case of high speed rail in Norway," Transportation Research Part A: Policy and Practice, Elsevier, vol. 78(C), pages 438-451.
    10. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    11. Chorus, Caspar G., 2014. "Benefit of adding an alternative to one׳s choice set: A regret minimization perspective," Journal of choice modelling, Elsevier, vol. 13(C), pages 49-59.
    12. Brücker, Herbert & Bertoli, Simone & Fernández-Huertas Moraga, Jesús, 2013. "The European Crisis and Migration to Germany: Expectations and the Diversion of Migration Flows," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79693, Verein für Socialpolitik / German Economic Association.
    13. Ye, Xin & Garikapati, Venu M. & You, Daehyun & Pendyala, Ram M., 2017. "A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 173-192.
    14. 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.
    15. Ton, Danique & Bekhor, Shlomo & Cats, Oded & Duives, Dorine C. & Hoogendoorn-Lanser, Sascha & Hoogendoorn, Serge P., 2020. "The experienced mode choice set and its determinants: Commuting trips in the Netherlands," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 744-758.
    16. Aydın Alptekinoğlu & John H. Semple, 2016. "The Exponomial Choice Model: A New Alternative for Assortment and Price Optimization," Operations Research, INFORMS, vol. 64(1), pages 79-93, February.
    17. Peter Davis & Pasquale Schiraldi, 2014. "The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products," RAND Journal of Economics, RAND Corporation, vol. 45(1), pages 32-63, March.
    18. Darren Hudson & Karina Gallardo & Terry Hanson, 2005. "Hypothetical (Non)Bias In Choice Experiments: Evidence From Freshwater Prawns," Experimental 0503003, University Library of Munich, Germany.
    19. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    20. Tao, Xuezong & Zhu, Lichao, 2020. "Meta-analysis of value of time in freight transportation: A comprehensive review based on discrete choice models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 138(C), pages 213-233.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:144:y:2006:i:1:p:287-300:10.1007/s10479-006-0015-x. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.