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Multinomial probit with structured covariance for route choice behavior

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  • Yai, Tetsuo
  • Iwakura, Seiji
  • Morichi, Shigeru
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    Abstract

    We propose another version of the multinomial probit model with a structured covariance matrix to represent any overlapped relation between route alternatives. The fundamental ideas of the model were presented in Yai et al. (1993) and Yai and Iwakura (1994). The assumptions introduced in the model may be more realistic for route choice behaviors on a dense network than the strict assumption of the independent alternative property of the multinomial logit model. As the nested logit model assumes an identical dispersion parameter between two modeling levels for all trip makers, the model has difficulty in expressing individual choice-tree structures. To improve the applicability of the multinomial probit model to route choice behaviors, we introduce a function which represents an overlapped relation between pairs of alternatives and propose a multinomial probit model in which the structured covariance matrix uses the function in order to consider the individual choice-tree structures in the matrix and the estimatability of the new alternative's covariances. After examining the applicability of the multinomial probit model using empirical route choice data in a Tokyo metropolitan region, we also propose a method for evaluating consumer benefits on complicated networks based on the multinomial probit model.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 31 (1997)
    Issue (Month): 3 (June)
    Pages: 195-207

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    Handle: RePEc:eee:transb:v:31:y:1997:i:3:p:195-207

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    References

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    1. C F Daganzo & Y Sheffi, 1982. "Multinomial probit with time-series data: unifying state dependence and serial correlation models," Environment and Planning A, Pion Ltd, London, vol. 14(10), pages 1377-1388, October.
    2. John Geweke & Michael Keane & David Runkle, 1994. "Alternative computational approaches to inference in the multinomial probit model," Staff Report 170, Federal Reserve Bank of Minneapolis.
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    4. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    5. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
    6. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
    7. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
    8. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
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    Cited by:
    1. Connors, Richard D. & Sumalee, Agachai & Watling, David P., 2007. "Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user-classes," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 593-615, July.
    2. Carlo Prato & Shlomo Bekhor & Cristina Pronello, 2012. "Latent variables and route choice behavior," Transportation, Springer, vol. 39(2), pages 299-319, March.
    3. Bekhor, Shlomo & Prato, Carlo Giacomo, 2009. "Methodological transferability in route choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 422-437, May.
    4. Castillo, Enrique & Menéndez, José María & Sánchez-Cambronero, Santos, 2008. "Predicting traffic flow using Bayesian networks," Transportation Research Part B: Methodological, Elsevier, vol. 42(5), pages 482-509, June.
    5. Frejinger, E. & Bierlaire, M. & Ben-Akiva, M., 2009. "Sampling of alternatives for route choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 984-994, December.
    6. Hu, Shucheng & Saleh, Wafaa, 2005. "Impacts of congestion charging on shopping trips in Edinburgh," Transport Policy, Elsevier, vol. 12(5), pages 443-450, September.
    7. Hironori Kato & Yuichiro Kaneko & Masashi Inoue, 2010. "Comparative analysis of transit assignment: evidence from urban railway system in the Tokyo Metropolitan Area," Transportation, Springer, vol. 37(5), pages 775-799, September.
    8. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    9. Liu, Yu-Hsin, 2011. "Incorporating scatter search and threshold accepting in finding maximum likelihood estimates for the multinomial probit model," European Journal of Operational Research, Elsevier, vol. 211(1), pages 130-138, May.
    10. Koppelman, Frank S. & Wen, Chieh-Hua, 1998. "Alternative nested logit models: structure, properties and estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 289-298, June.
    11. Clark, Stephen D. & Watling, David P., 2002. "Sensitivity analysis of the probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 617-635, August.
    12. Castillo, Enrique & Menéndez, José María & Jiménez, Pilar & Rivas, Ana, 2008. "Closed form expressions for choice probabilities in the Weibull case," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 373-380, May.
    13. Philip Yu, 2000. "Bayesian analysis of order-statistics models for ranking data," Psychometrika, Springer, vol. 65(3), pages 281-299, September.
    14. Cohen, Michael, 2010. "A Structured Covariance Probit Demand Model," Research Reports 149970, University of Connecticut, Food Marketing Policy Center.
    15. Daisuke Fukuda & Tetsuo Yai, 2010. "Semiparametric specification of the utility function in a travel mode choice model," Transportation, Springer, vol. 37(2), pages 221-238, March.
    16. Habib, Khandker Nurul & Morency, Catherine & Trépanier, Martin & Salem, Sarah, 2013. "Application of an independent availability logit model (IAL) for route choice modelling: Considering bridge choice as a key determinant of selected routes for commuting in Montreal," Journal of choice modelling, Elsevier, vol. 9(C), pages 14-26.
    17. Frejinger, E. & Bierlaire, M., 2007. "Capturing correlation with subnetworks in route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 363-378, March.

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