IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v4y1972i2p205-233.html
   My bibliography  Save this article

The Calibration of Gravity, Entropy, and Related Models of Spatial Interaction

Author

Listed:
  • M Batty

    (Urban Systems Research Unit, Department of Geography, University of Reading, Reading, England)

  • S Mackie

    (Local Government Operational Research Unit, Reading, England)

Abstract

This paper presents a methodology for deriving best statistics for the calibration of spatial interaction models, and several procedures for finding best parameter values are described. The family of spatial interaction models due to Wilson is first outlined, and then some existing calibration methods are briefly reviewed. A procedure for deriving best statistics based on the principle of maximum-likelihood is then developed from the work of Hyman and Evans, and the methodology is illustrated using the example of a retail gravity model. Five methods for solving the maximum-likelihood equations are outlined: procedures based on a simple first-order iterative process, the Newton—Raphson method for several variables, multivariate Fibonacci search, search using the Simplex method, and search based on quadratic convergence, are all tested and compared. It appears that the Newton—Raphson method is the most efficient, and this is further tested in the calibration of disaggregated residential location models.

Suggested Citation

  • M Batty & S Mackie, 1972. "The Calibration of Gravity, Entropy, and Related Models of Spatial Interaction," Environment and Planning A, , vol. 4(2), pages 205-233, June.
  • Handle: RePEc:sae:envira:v:4:y:1972:i:2:p:205-233
    DOI: 10.1068/a040205
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a040205
    Download Restriction: no

    File URL: https://libkey.io/10.1068/a040205?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cabrera Delgado, Jorge & Bonnel, Patrick, 2016. "Level of aggregation of zoning and temporal transferability of the gravity distribution model: The case of Lyon," Journal of Transport Geography, Elsevier, vol. 51(C), pages 17-26.
    2. Shiwei Lu & Shih-Lung Shaw & Zhixiang Fang & Xirui Zhang & Ling Yin, 2017. "Exploring the Effects of Sampling Locations for Calibrating the Huff Model Using Mobile Phone Location Data," Sustainability, MDPI, vol. 9(1), pages 1-18, January.
    3. Shen, Yao, 2019. "Segregation through space: A scope of the flow-based spatial interaction model," Journal of Transport Geography, Elsevier, vol. 76(C), pages 10-23.
    4. Mozolin, M. & Thill, J. -C. & Lynn Usery, E., 2000. "Trip distribution forecasting with multilayer perceptron neural networks: A critical evaluation," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 53-73, January.
    5. Cho, Cheol-Joo, 1998. "An equity-efficiency trade-off model for the optimum location of medical care facilities," Socio-Economic Planning Sciences, Elsevier, vol. 32(2), pages 99-112, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envira:v:4:y:1972:i:2:p:205-233. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.