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

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  • 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
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    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. 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.
    3. 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.
    4. 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.
    5. 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.

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