Some developments on the cross-nested logit model
In this paper the cross-nested logit (CNL) model is reformulated as a generalization of the two levels hierarchical logit model. The proposed analytical formulation is derived from the GEV model. Moreover, a general expression of the covariance matrix of the CNL model presenting interesting empirical evidence is proposed. It will be also demonstrated that it is generally possible to specify the model so that this general expression reproduces any given hypothetical homoscedastic covariance matrix. Hence, from the latter, not just probit or mixed multinomial logit choice probabilities (through some simulation methods, e.g. Montecarlo) but also CNL choice probabilities (with a closed analytical form) could be derived. Moreover, comparisons among CNL and probit choice probabilities are presented and the resulting similarity indicates that the CNL is a very interesting closed form alternative to the more flexible non-closed form models.
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Volume (Year): 38 (2004)
Issue (Month): 9 (November)
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- 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.
- Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
- H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
- Cascetta, Ennio & Papola, Andrea, 2003. "A joint mode-transit service choice model incorporating the effect of regional transport service timetables," Transportation Research Part B: Methodological, Elsevier, vol. 37(7), pages 595-614, August.
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