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Variances and covariances for origin-destination flows when estimated by log-linear models

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  • Bell, M. G. H.

Abstract

An expression is derived for the variances and covariances of the logarithms of origin- destination flows when estimated by one of a family of log-linear models. Among this family is the Furness growth factor model, the gravity model, the Willumsen model and the Van Zuylen-Bell model. Variances and covariances for the logarithms of the parameters incorporating prior information and for the values of the constraints with which the fitted values must conform are transformed linearly into approximate variances and covariances for the logarithms of the fitted values. Additional error due to misspecification of either the model or the constraints is not taken into account. Depending on the model, the prior information parameters may correspond to values of a deterrence function or to a base year trip matrix, while the constraints may represent design year trip end totals or traffic counts. As an illustration, the expression is applied to an example involving Willumsen's model.

Suggested Citation

  • Bell, M. G. H., 1985. "Variances and covariances for origin-destination flows when estimated by log-linear models," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 497-507, December.
    • Handle: RePEc:eee:transb:v:19:y:1985:i:6:p:497-507
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    Cited by:

    1. Xuesong Zhou & George F. List, 2010. "An Information-Theoretic Sensor Location Model for Traffic Origin-Destination Demand Estimation Applications," Transportation Science, INFORMS, vol. 44(2), pages 254-273, May.
    2. Xie, Chi & Kockelman, Kara M. & Waller, S. Travis, 2011. "A maximum entropy-least squares estimator for elastic origin–destination trip matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1465-1482.

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