localG
G and Gstar local spatial statistics
The local spatial statistic G is calculated for each zone based on the spatial weights object used. The value returned is a Zvalue, and may be used as a diagnostic tool. High positive values indicate the posibility of a local cluster of high values of the variable being analysed, very low relative values a similar cluster of low values. For inference, a Bonferronitype test is suggested in the references, where tables of critical values may be found (see also details below).
 Keywords
 spatial
Usage
localG(x, listw, zero.policy=NULL, spChk=NULL)
Arguments
 x
 a numeric vector the same length as the neighbours list in listw
 listw
 a
listw
object created for example bynb2listw
 zero.policy
 default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
 spChk
 should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use
get.spChkOption()
Details
If the neighbours member of listw has a "self.included" attribute set
to TRUE, the Gstar variant, including the selfweight $w_{ii} > 0$,
is calculated and returned. The returned vector will have a "gstari"
attribute set to TRUE. Selfweights can be included by using the
include.self
function in the spweights package before converting
the neighbour list to a spatial weights list with nb2listw
as
shown below in the example.
The critical values of the statistic under assumptions given in the references for the 95th percentile are for n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.
Value

A vector of G or Gstar values, with attributes "gstari" set to TRUE or
FALSE, "call" set to the function call, and class "localG".
References
Ord, J. K. and Getis, A. 1995 Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27, 286306; Getis, A. and Ord, J. K. 1996 Local spatial statistics: an overview. In P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment (Cambridge: Geoinformation International), 261277.
Examples
data(getisord)
xycoords < cbind(xyz$x, xyz$y)
nb30 < dnearneigh(xycoords, 0, 30)
G30 < localG(xyz$val, nb2listw(nb30, style="B"))
G30[length(xyz$val)136]
nb60 < dnearneigh(xycoords, 0, 60)
G60 < localG(xyz$val, nb2listw(nb60, style="B"))
G60[length(xyz$val)136]
nb90 < dnearneigh(xycoords, 0, 90)
G90 < localG(xyz$val, nb2listw(nb90, style="B"))
G90[length(xyz$val)136]
nb120 < dnearneigh(xycoords, 0, 120)
G120 < localG(xyz$val, nb2listw(nb120, style="B"))
G120[length(xyz$val)136]
nb150 < dnearneigh(xycoords, 0, 150)
G150 < localG(xyz$val, nb2listw(nb150, style="B"))
G150[length(xyz$val)136]
brks < seq(5,5,1)
cm.col < cm.colors(length(brks)1)
image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),
breaks=brks, col=cm.col, asp=1)
text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7)
polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
title(main=expression(paste("Values of the ", G[i], " statistic")))
G30s < localG(xyz$val, nb2listw(include.self(nb30),
style="B"))
cat("value according to Getis and Ord's eq. 14.2, p. 263 (1996)\n")
G30s[length(xyz$val)136]
cat(paste("value given by Getis and Ord (1996), p. 267",
"(division by n1 rather than n \n in variance)\n"))
G30s[length(xyz$val)136] *
(sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /
sqrt(var(xyz$val)))
image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),
breaks=brks, col=cm.col, asp=1)
text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7)
polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
title(main=expression(paste("Values of the ", G[i]^"*", " statistic")))