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A Note on the Extremities of Local Moran's I i s and Their Impact on Global Moran's I
Author(s) -
Tiefelsdorf Michael,
Boots Barry
Publication year - 1997
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1997.tb00960.x
Subject(s) - spatial analysis , statistic , contrast (vision) , statistics , spatial dependence , spatial econometrics , mathematics , geography , econometrics , computer science , artificial intelligence
By defining local Moran's I i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I i expressed by the local linkage degree. Depending on whether we use the W‐ or C‐ coding of the spatial connectivity matrix, the variance of local Moran's I i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I i with a small variance. Counterintuitively, global Moran's I defined in the W‐ coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C‐ coding. Second, we investigate the impact of the empirical data on local Moran's I i and show that local Moran's I i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I i . Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation .