1\name{gearyc}
2
3\alias{gearyc}
4
5\title{Geary's C Autocorrelation Statistic}
6
7
8\description{
9Geary's c statistic is used to measure autocorrelation between areas within
10a region, as follows:
11
12\deqn{
13c=\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}
14}{
15c = (n-1) [sum_i sum_j W_ij (Z_i-Z_j)^2]/[2(sum_i sum_j W_ij) sum_k (Z_k-mean({Z))^2}
16}
17
18\eqn{W}{W} is a squared matrix which represents the relationship between each
19pair of regions. An usual approach is set \eqn{w_{ij}}{w_ij} to 1 if regions
20\eqn{i}{i} and \eqn{j}{j} have a common boundary and 0 otherwise, or it may
21represent the inverse distance between the centroids of that two regions.
22
23Small values of this statistic may indicate the presence of highly
24correlated areas, which may be a cluster.
25}
26
27
28\seealso{
29DCluster, gearyc.stat, gearyc.boot, gearyc.pboot
30}
31
32\references{
33Geary, R. C. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician 5, 115-145.
34}
35
36\keyword{spatial}
37