gearyc {DCluster}

Geary's C Autocorrelation Statistic

Description

Geary's c statistic is used to measure autocorrelation between areas within a region, as follows:

c=\frac{(n-1)\sum_i \sum_j W_{ij}(Z_i-Z_j)^2}{2(\sum_i\sum_jW_{ij})\sum_k (Z_k-\overline{Z})^2}

W is a squared matrix which represents the relationship between each pair of regions. An usual approach is set w_{ij} to 1 if regions i and j have a common boundary and 0 otherwise, or it may represent the inverse distance between the centroids of that two regions.

Small values of this statistic may indicate the presence of highly correlated areas, which may be a cluster.

References

Geary, R. C. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician 5, 115-145.

See Also

DCluster, gearyc.stat, gearyc.boot, gearyc.pboot