Local and Global Spatial Statistics

Synonyms

Getis-Ord index G*; LISA statistics; Local Indicators of Spatial Association statistics; Local Moran's I; Statistics, spatial

Definition

These statistics assess the clustering of spatial data at the local level (using local clusters) or globally (using all the available data).

Main Text

Moran's I and Geary's C are global indices of spatial association that include all the locations in the data. A spatial contiguity matrix W _ij , with a zero diagonal, and the off-diagonal non-zero elements indicating contiguity of locations i and j are used to code proximities. The most commonly used global indicators of spatial autocorrelation are Moran's I and Geary's C which are defined as:

$$ I=\frac{N\sum\nolimits_i {\sum\nolimits_j{W_{ij}Z_i Z_j}}} {\sum\nolimits_i {\sum\nolimits_i{W_{ij}}} \sum\nolimits_i{Z_i^2}}\:, $$

(1)

$$ C=\frac{(N-1)\sum\nolimits_i{\sum\nolimits_j{W_{ij}(x_i -x_j)^2}}} {2(\sum\nolimits_i {\sum\nolimits_j{W_{ij}}}) \sum\nolimits_i{Z_i^2}}\:. $$

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