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A Generalized Significance Testing Method for Global Measures of Spatial Association: An Extension of the Mantel Test

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  • Sang-Il Lee

    (Department of Geography Education, Seoul National University, San 56-1, Sillim-Dong, Gwanak-Gu, Seoul 151-742, South Korea)

Abstract

This research is concerned with providing a generalized significance testing method for global measures of spatial association by extending the Mantel test. Even though it has long been recognized that univariate spatial association measures such as Moran's I and Geary's c are special cases of Mantel's generalized association statistic, an intensive and comprehensive examination of the connections, particularly in terms of significance testing has never been undertaken. Furthermore, researchers have faced difficulties in dealing with spatial weights matrices with nonzero diagonal elements, and establishing the significance testing method for bivariate spatial association measures such as Cross–Moran and Lee's L. The author demonstrates that the proposed extended Mantel test can be applied to any global measure of spatial association with any form of spatial weights matrix in order to approximate the first two moments of the measures. A Monte Carlo simulation for each measure with various forms of spatial weights matrices confirms the exactness of the approximation.

Suggested Citation

  • Sang-Il Lee, 2004. "A Generalized Significance Testing Method for Global Measures of Spatial Association: An Extension of the Mantel Test," Environment and Planning A, , vol. 36(9), pages 1687-1703, September.
    • Handle: RePEc:sae:envira:v:36:y:2004:i:9:p:1687-1703
    DOI: 10.1068/a34143
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    References listed on IDEAS

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    1. J. Keith Ord & Arthur Getis, 2001. "Testing for Local Spatial Autocorrelation in the Presence of Global Autocorrelation," Journal of Regional Science, Wiley Blackwell, vol. 41(3), pages 411-432, August.
    2. Griffith, Daniel A. & Layne, Larry J., 1999. "A Casebook for Spatial Statistical Data Analysis: A Compilation of Different Thematic Data Sets," OUP Catalogue, Oxford University Press, number 9780195109580.
    3. Kelejian, Harry H. & Robinson, Dennis P., 1998. "A suggested test for spatial autocorrelation and/or heteroskedasticity and corresponding Monte Carlo results," Regional Science and Urban Economics, Elsevier, vol. 28(4), pages 389-417, July.
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    Cited by:

    1. Zhang, Tonglin & Lin, Ge, 2007. "A decomposition of Moran's I for clustering detection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6123-6137, August.
    2. Bell, Adrian V. & Rader, Russell B. & Peck, Steven L. & Sih, Andrew, 2009. "The positive effects of negative interactions: Can avoidance of competitors or predators increase resource sampling by prey?," Theoretical Population Biology, Elsevier, vol. 76(1), pages 52-58.
    3. Tonglin Zhang & Ge Lin, 2008. "Identification of local clusters for count data: a model-based Moran's I test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 293-306.

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