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Incorporating variance and covariance heterogeneity in the Generalized Nested Logit model: an application to modeling long distance travel choice behavior

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  • Koppelman, Frank S.
  • Sethi, Vaneet

Abstract

The assumption of independently and identically distributed (IID) error terms in the Multinomial Logit (MNL) model leads to its infamous IIA property. Relaxation of the IID assumption has been undertaken along a number of isolated dimensions leading to the development of a rich set of discrete choice models, that are more flexible than the MNL model. In some cases, these more general models lose the mathematically convenient closed-form structure of the MNL. In this paper, we combine the most flexible isolated closed-form extensions of the MNL and Nested Logit (NL) models in an integrated model structure to yield a behaviorally rich, yet computationally tractable choice model. Specifically, we combine the Generalized Nested Logit model that allows for non-independent errors, the Heteroscedastic MNL which allows non-constant errors across observations, and the Covariance Heterogeneous NL model which allows for non-constant correlation structure across observations. The resulting model, called the Heterogeous GNL model extends our ability to represent the complex behavioral processes involved in choice decision-making. The value and need for the additional modeling complexity of the HGNL model is tested in the empirical context of mode and rail service class choice behavior for long distance intercity travel. An incremental modeling approach is adopted, i.e., we start from the simple MNL model and sequentially relax some of its restrictive assumptions to estimate progressively more flexible model structures. The statistical fit and behavioral appeal of the estimated models improve substantially with each additional relaxation, strongly supporting the concept of integrating isolated generalizations.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transb:v:39:y:2005:i:9:p:825-853
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    References listed on IDEAS

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    1. 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.
    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. Williams, H. C. W. L. & Ortuzar, J. D., 1982. "Behavioural theories of dispersion and the mis-specification of travel demand models," Transportation Research Part B: Methodological, Elsevier, vol. 16(3), pages 167-219, June.
    4. 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.
    5. Swait, Joffre & Adamowicz, Wiktor, 2001. "Choice Environment, Market Complexity, and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 141-167, November.
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    1. Smirnov, Oleg A. & Egan, Kevin J., 2012. "Spatial random utility model with an application to recreation demand," Economic Modelling, Elsevier, vol. 29(1), pages 72-78.
    2. Arbués, Pelayo & Baños, José F. & Mayor, Matías & Suárez, Patricia, 2016. "Determinants of ground transport modal choice in long-distance trips in Spain," Transportation Research Part A: Policy and Practice, Elsevier, vol. 84(C), pages 131-143.
    3. Koo, Tay T.R. & Wu, Cheng-Lung (Richard) & Dwyer, Larry, 2010. "Ground travel mode choices of air arrivals at regional destinations: The significance of tourism attributes and destination contexts," Research in Transportation Economics, Elsevier, vol. 26(1), pages 44-53.
    4. Fosgerau, M. & Bierlaire, M., 2009. "Discrete choice models with multiplicative error terms," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 494-505, June.
    5. Hough, Gary & Hassanien, Ahmed, 2010. "Transport choice behaviour of Chinese and Australian tourists in Scotland," Research in Transportation Economics, Elsevier, vol. 26(1), pages 54-65.
    6. 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.
    7. Stephane Hess & Denis Bolduc & John Polak, 2010. "Random covariance heterogeneity in discrete choice models," Transportation, Springer, vol. 37(3), pages 391-411, May.
    8. de Moraes Ramos, Giselle & Daamen, Winnie & Hoogendoorn, Serge, 2013. "Modelling travellers' heterogeneous route choice behaviour as prospect maximizers," Journal of choice modelling, Elsevier, vol. 6(C), pages 17-33.
    9. Sobolewski, Maciej & Czajkowski, MikoŁaj, 2012. "Network effects and preference heterogeneity in the case of mobile telecommunications markets," Telecommunications Policy, Elsevier, vol. 36(3), pages 197-211.
    10. Ahmadi Azari, Kian & Arintono, Sulistyo & Hamid, Hussain & Rahmat, Riza Atiq O.K., 2013. "Modelling demand under parking and cordon pricing policy," Transport Policy, Elsevier, vol. 25(C), pages 1-9.
    11. repec:eee:transa:v:106:y:2017:i:c:p:89-99 is not listed on IDEAS
    12. Smirnov, Oleg A., 2010. "Modeling spatial discrete choice," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 292-298, September.
    13. Fosgerau, Mogens & Bierlaire, Michel, 2007. "Circumventing the problem of the scale: discrete choice models with multiplicative error terms," MPRA Paper 3901, University Library of Munich, Germany.
    14. Caleb Van Nostrand & Vijayaraghavan Sivaraman & Abdul Pinjari, 2013. "Analysis of long-distance vacation travel demand in the United States: a multiple discrete–continuous choice framework," Transportation, Springer, vol. 40(1), pages 151-171, January.
    15. Simona Rasciute & Sean Puckett & Eric J. Pentecost, 2015. "The Allocation Of Oecd Direct Investment Between Ceecs: A Discrete Choice Approach," Bulletin of Economic Research, Wiley Blackwell, vol. 67(S1), pages 26-39, December.
    16. Nakayama, Shoichiro & Chikaraishi, Makoto, 2015. "Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 672-685.

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