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Estimation of Parameters of Network Equilibrium Models: A Maximum Likelihood Method and Statistical Properties of Network Flow

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Shoichiro Nakayama

    (Kanazawa University, Japan and University of Leeds)

  • Richard D.

    (Connors and David Watling, University of Leeds)

Abstract

Estimation of the parameters in network equilibrium models, including OD matrix elements, is essential when applying the models to real-world networks. Link flow data are convenient for estimating parameters because it is relatively easy for us to obtain them. In this study, we propose a maximum likelihood method for estimating parameters of network equilibrium models using link flow data, and derive first and second derivatives of the likelihood function under the equilibrium constraint. Using the likelihood function and its derivatives, t-values and other statistical indices are provided to examine the confidence interval of estimated parameters and the model’s goodness-of-fit. Also, we examine which conditions are needed for consistency, asymptotic efficiency, and asymptotic normality for the maximum likelihood estimators with non-I.I.D. link flow data. In order to investigate the validity and applicability, the proposed ML method is applied to a simple network and the road network in Kanazawa City, Japan.

Suggested Citation

  • Shoichiro Nakayama & Richard D., 2009. "Estimation of Parameters of Network Equilibrium Models: A Maximum Likelihood Method and Statistical Properties of Network Flow," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 39-56, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_3
    DOI: 10.1007/978-1-4419-0820-9_3
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    Cited by:

    1. Siripirote, Treerapot & Sumalee, Agachai & Ho, H.W. & Lam, William H.K., 2015. "Statistical approach for activity-based model calibration based on plate scanning and traffic counts data," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 280-300.
    2. Teppei Kato & Kenetsu Uchida & William H. K. Lam & Agachai Sumalee, 2021. "Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network," Transportation, Springer, vol. 48(4), pages 1639-1670, August.

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