Statistical Test for Local Patterns of Spatial Association

Yee Leung, Chang-Lin Mei and Wen-Xiu Zhang
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Yee Leung: Department of Geography and Resource Management, Center for Environmental Policy and Resource Management, and Joint Laboratory for Geoinformation Science, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China

Environment and Planning A, 2003, vol. 35, issue 4, 725-744

Abstract: In recent years, there has been a growing interest in the use of local measures such as Anselin's LISAs and Ord and Getis G statistics to identify local patterns of spatial association. The statistical significance test based on local statistics is one of the most important aspects in performing this kind of analysis, and a randomized permutation approach and normal approximation are commonly used to derive the p -values of the statistics. To circumvent some of the shortcomings of these existing methods and to offer a more formal approach in line with classical statistical framework, we develop in this paper an exact method for computing the p -values of the local Moran's I i , local Geary's c i , and the modified Ord and Getis G statistics based on the distributional theory of quadratic forms in normal variables. Furthermore, an approximate method, called three-moment χ 2 approximation, with explicit calculation formulae is also proposed to achieve a computational cost lower than the exact method. Numerical evaluation on the accuracy of the approximate null distributions of the local statistics demonstrates that the proposed three-moment χ 2 method is useful in some situations although it is inappropriate for approximating the null distribution of I i . The study not only provides an exact test for local patterns of spatial association, but also put the tests of several local statistics within a unified statistical framework.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:sae:envira:v:35:y:2003:i:4:p:725-744

DOI: 10.1068/a3550

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