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

  • Shoichiro Nakayama
  • Richard D.


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.


Central Limit Theorem Maximum Likelihood Method Route Choice Transportation Research Part Asymptotic Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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I would like to express my gratitude to Prof. Jun-ichi Takayama (Kanazawa University) for providing valuable comments and advices. I am also grateful to Mr. Tomonari Anaguchi (Kanazawa University) for his computational support.


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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Shoichiro Nakayama
    • 1
  • Richard D.
    • 2
  1. 1.Kanazawa University, Japan and University of LeedsBritainU.K
  2. 2.Connors and David Watling, University of LeedsBritainU.K

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