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 Z-value, 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 Bonferroni-type test is suggested in the references, where tables of critical values may be found (see also details below).
localG(x, listw, zero.policy=NULL, spChk=NULL, return_internals=FALSE, GeoDa=FALSE) localG_perm(x, listw, nsim=499, zero.policy=NULL, spChk=NULL, return_internals=FALSE, iseed=NULL)
x |
a numeric vector the same length as the neighbours list in listw |
listw |
a |
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 |
return_internals |
default FALSE, if TRUE, return internal values of G, EI and VG as as attribute matrix |
GeoDa |
default FALSE, if TRUE, drop x values for no-neighbour and self-neighbour only observations from all summations |
nsim |
default 499, number of conditonal permutation simulations |
iseed |
default NULL, used to set the seed for possible parallel RNGs |
If the neighbours member of listw has a "self.included" attribute set
to TRUE, the Gstar variant, including the self-weight w_{ii} > 0,
is calculated and returned. The returned vector will have a "gstari"
attribute set to TRUE. Self-weights can be included by using the
include.self function 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.
A vector of G or Gstar values, with attributes "gstari" set to TRUE or FALSE, "call" set to the function call, and class "localG".
Conditional permutations added for comparative purposes; permutations are over the whole data vector omitting the observation itself.
Roger Bivand Roger.Bivand@nhh.no
Ord, J. K. and Getis, A. 1995 Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27, 286–306; 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), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi: 10.1007/s11749-018-0599-x
data(getisord, package="spData")
# spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to
# avoid putting these objects into the global environment via lazy loading
if (exists("go_xyz") && packageVersion("spData") >= "0.3.2") {
xyz <- go_xyz
x <- go_x
y <- go_y
}
xycoords <- cbind(xyz$x, xyz$y)
nb30 <- dnearneigh(xycoords, 0, 30)
G30 <- localG(xyz$val, nb2listw(nb30, style="B"))
G30[length(xyz$val)-136]
set.seed(1)
G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style="B"))
G30_sim[length(xyz$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 n-1 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")))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.