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The continuous cross-nested logit model: Formulation and application for departure time choice

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  • Lemp, Jason D.
  • Kockelman, Kara M.
  • Damien, Paul

Abstract

Discrete choice models, like the multinomial logit (MNL), have long been recognized for their ability to capture a wide array of transport-related choice phenomena. However, a number of choices are continuous response variables (e.g., location, departure time, activity duration, and vehicle usage). This paper introduces the continuous cross-nested logit (CCNL) model. The CCNL model results from generalizing the discrete cross-nested logit (CNL) model for a continuous response variable, much like the continuous logit model emerges by generalizing the MNL. The model is formulated and shown to come from the generalized extreme value (GEV) class of models. In addition, the structure of utility correlations is presented. The model's parameters are estimated for a work-tour departure time context using Bayesian estimation techniques and San Francisco Bay Area data. Empirical results suggest model predictions that are very similar to the continuous logit, but it out-performs the continuous logit in terms of out-of-sample prediction with these data. The CCNL also allows a more flexible choice behavior to emerge. Finally, a simple welfare example is illustrated and a number of model extensions are presented.

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  • 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.
    • Handle: RePEc:eee:transb:v:44:y:2010:i:5:p:646-661
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    1. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-424, March.
    2. Brownstone, David & Small, Kenneth A., 2005. "Valuing time and reliability: assessing the evidence from road pricing demonstrations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(4), pages 279-293, May.
    3. 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.
    4. Michel Bierlaire, 2006. "A theoretical analysis of the cross-nested logit model," Annals of Operations Research, Springer, vol. 144(1), pages 287-300, April.
    5. Stephane Hess & John Polak & Andrew Daly & Geoffrey Hyman, 2007. "Flexible substitution patterns in models of mode and time of day choice: new evidence from the UK and the Netherlands," Transportation, Springer, vol. 34(2), pages 213-238, March.
    6. Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
    7. de Jong, Gerard & Daly, Andrew & Pieters, Marits & Vellay, Carine & Bradley, Mark & Hofman, Frank, 2003. "A model for time of day and mode choice using error components logit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 39(3), pages 245-268, May.
    8. 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.
    9. 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.
    10. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    11. Bhat, Chandra R. & Steed, Jennifer L., 2002. "A continuous-time model of departure time choice for urban shopping trips," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 207-224, March.
    12. 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.
    13. Wang, James Jixian, 1996. "Timing utility of daily activities and its impact on travel," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(3), pages 189-206, May.
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    4. Brey, Raúl & Walker, Joan L., 2011. "Latent temporal preferences: An application to airline travel," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 880-895, November.
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    6. Ricardo A. Daziano & Luis Miranda-Moreno & Shahram Heydari, 2013. "Computational Bayesian Statistics in Transportation Modeling: From Road Safety Analysis to Discrete Choice," Transport Reviews, Taylor & Francis Journals, vol. 33(5), pages 570-592, September.
    7. 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.
    8. Jason D. Lemp & Kara M. Kockelman & Paul Damien, 2012. "A Bivariate Multinomial Probit Model for Trip Scheduling: Bayesian Analysis of the Work Tour," Transportation Science, INFORMS, vol. 46(3), pages 405-424, August.
    9. Thierry Delahaye & Rodrigo Acuna-Agost & Nicolas Bondoux & Anh-Quan Nguyen & Mourad Boudia, 2017. "Data-driven models for itinerary preferences of air travelers and application for dynamic pricing optimization," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 16(6), pages 621-639, December.
    10. Zheng Zhu & Xiqun Chen & Chenfeng Xiong & Lei Zhang, 2018. "A mixed Bayesian network for two-dimensional decision modeling of departure time and mode choice," Transportation, Springer, vol. 45(5), pages 1499-1522, September.
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    12. 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.
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