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Normalization and correlation of cross-nested logit models

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  • Abbe, E.
  • Bierlaire, M.
  • Toledo, T.

Abstract

We address two fundamental issues associated with the use of cross-nested logit models. On the one hand, we justify the adequate normalization of the model proposed by Wen and Koppelman [Wen, C.-H., Koppelman, F.S., 2001. The generalized nested logit model. Transportation Research Part B 35(7), 627-641]. On the other hand, we provide an analysis of the correlation structure of the CNL, based on random utility theory. We evaluate the validity of the approximation proposed by Papola [Papola, A., 2004. Some developments on the cross-nested logit model. Transportation Research B 38(9), 833-851], both using theoretical arguments and numerical examples based on the exact formula of the correlation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:41:y:2007:i:7:p:795-808
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    References listed on IDEAS

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    5. 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.
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    Cited by:

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    4. 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.
    5. Julie Poirier, 2012. "How to Deal with Protest Bids and Preference for the Status Quo in Choice Experiments ?," Working Papers 2012-02, Center for Research in Economics and Statistics.
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    7. 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.
    8. 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.
    9. Marzano, Vittorio, 2014. "A simple procedure for the calculation of the covariances of any Generalized Extreme Value model," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 151-162.
    10. Newman, Jeffrey P., 2008. "Normalization of network generalized extreme value models," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 958-969, December.
    11. Alessandro Iaria, & Wang, Ao, 2021. "An Empirical Model of Quantity Discounts with Large Choice Sets," The Warwick Economics Research Paper Series (TWERPS) 1378, University of Warwick, Department of Economics.
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    13. Drabas, Tomasz & Wu, Cheng-Lung, 2013. "Modelling air carrier choices with a Segment Specific Cross Nested Logit model," Journal of Air Transport Management, Elsevier, vol. 32(C), pages 8-16.
    14. Lemp, Jason D. & Kockelman, Kara M. & Damien, Paul, 2010. "The continuous cross-nested logit model: Formulation and application for departure time choice," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 646-661, June.
    15. Fiore Tinessa & Vittorio Marzano & Andrea Papola, 2021. "Choice probabilities and correlations in closed-form route choice models: specifications and drawbacks," Papers 2110.07224, arXiv.org.
    16. Robin, Th. & Antonini, G. & Bierlaire, M. & Cruz, J., 2009. "Specification, estimation and validation of a pedestrian walking behavior model," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 36-56, January.
    17. Anna Fernández-Antolín & Matthieu Lapparent & Michel Bierlaire, 2018. "Modeling purchases of new cars: an analysis of the 2014 French market," Theory and Decision, Springer, vol. 84(2), pages 277-303, March.
    18. 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.
    19. Astegiano, Paola & Akinc, Deniz & Himpe, Willem & Tampère, Chris M.J. & Vandebroek, Martina, 2017. "Quantifying the explanatory power of mobility-related attributes in explaining vehicle ownership decisions," Research in Transportation Economics, Elsevier, vol. 66(C), pages 2-11.
    20. Liu, Yan & Cirillo, Cinzia, 2018. "A generalized dynamic discrete choice model for green vehicle adoption," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PB), pages 288-302.
    21. Haghani, Milad & Sarvi, Majid & Shahhoseini, Zahra, 2015. "Accommodating taste heterogeneity and desired substitution pattern in exit choices of pedestrian crowd evacuees using a mixed nested logit model," Journal of choice modelling, Elsevier, vol. 16(C), pages 58-68.
    22. Gu, Yu & Chen, Anthony & Kitthamkesorn, Songyot, 2022. "Weibit choice models: Properties, mode choice application and graphical illustrations," Journal of choice modelling, Elsevier, vol. 44(C).
    23. 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.
    24. Sener, Ipek N. & Pendyala, Ram M. & Bhat, Chandra R., 2011. "Accommodating spatial correlation across choice alternatives in discrete choice models: an application to modeling residential location choice behavior," Journal of Transport Geography, Elsevier, vol. 19(2), pages 294-303.
    25. Perez-Lopez, Jose-Benito & Novales, Margarita & Orro, Alfonso, 2022. "Spatially correlated nested logit model for spatial location choice," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 1-12.

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