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Testing spatial autocorrelation in weighted networks: the modes permutation test

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  • François Bavaud

Abstract

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardized exchange matrix appearing in spectral clustering and generalize to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an accessibility matrix into an exchange matrix with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • François Bavaud, 2013. "Testing spatial autocorrelation in weighted networks: the modes permutation test," Journal of Geographical Systems, Springer, vol. 15(3), pages 233-247, July.
    • Handle: RePEc:kap:jgeosy:v:15:y:2013:i:3:p:233-247
    DOI: 10.1007/s10109-013-0179-2
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    References listed on IDEAS

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    1. Yongwan Chun, 2008. "Modeling network autocorrelation within migration flows by eigenvector spatial filtering," Journal of Geographical Systems, Springer, vol. 10(4), pages 317-344, December.
    2. Julian Besag & Peter J. Diggle, 1977. "Simple Monte Carlo Tests for Spatial Pattern," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 327-333, November.
    3. M F Goodchild & T R Smith, 1980. "Intransitivity, the Spatial Interaction Model, and US Migration Streams," Environment and Planning A, , vol. 12(10), pages 1131-1144, October.
    4. Daniel A. Griffith, 2003. "Spatial Autocorrelation and Spatial Filtering," Advances in Spatial Science, Springer, number 978-3-540-24806-4.
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    Cited by:

    1. Bavaud, François, 2023. "Exact first moments of the RV coefficient by invariant orthogonal integration," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Qing Luo & Daniel A. Griffith & Huayi Wu, 2019. "Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics," Journal of Geographical Systems, Springer, vol. 21(2), pages 237-269, June.
    3. F. Bavaud & M. Kordi & C. Kaiser, 2018. "Flow autocorrelation: a dyadic approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 61(1), pages 95-111, July.

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    More about this item

    Keywords

    Bootstrap; Local variance; Markov and semi-Markov processes; Moran’s I ; Permutation test; Spatial autocorrelation; Spatial filtering; Weighted networks; C12; C15; C31;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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