Compute Geary's C

A simple function to compute Geary's C, called by geary.test and geary.mc; $$C = \frac{(n-1)}{2\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\sum_{i=1}^{n}(x_i - \bar{x})^2} $$ geary.intern is an internal function used to vary the similarity criterion.

Usage

geary(x, listw, n, n1, S0, zero.policy=attr(listw, "zero.policy"), scale=TRUE)
<!-- %geary.intern(x, listw, n, zero.policy, type="geary") -->

Arguments

x: a numeric vector the same length as the neighbours list in listw
listw: a listw object created for example by nb2listw
n: number of zones
n1: n - 1
S0: global sum of weights
zero.policy: default attr(listw, "zero.policy") as set when listw was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

scale: default TRUE, may be FALSE to revert changes made to accommodate localC in November 2021 (see #151)

Value

a list with

C: Geary's C
K: sample kurtosis of x

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.

Author

Roger Bivand Roger.Bivand@nhh.no

Examples

data(oldcol)
col.W <- nb2listw(COL.nb, style="W")
str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1,
 Szero(col.W)))
#> List of 2
#>  $ C: num 0.53
#>  $ K: num 2.23