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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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    4. Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
    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.
    6. Michel Bierlaire, 2006. "A theoretical analysis of the cross-nested logit model," Annals of Operations Research, Springer, vol. 144(1), pages 287-300, April.
    7. 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.
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