spdep (version 1.3-7)

globalG.test: Global G test for spatial autocorrelation

Description

The global G statistic for spatial autocorrelation, complementing the local Gi LISA measures: localG.

Usage

globalG.test(x, listw, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE,
 na.action=na.fail)

Value

A list with class htest containing the following components:

statistic

the value of the standard deviate of Getis-Ord G.

p.value

the p-value of the test.

estimate

the value of the observed statistic, its expectation and variance.

alternative

a character string describing the alternative hypothesis.

data.name

a character string giving the name(s) of the data.

Arguments

x

a numeric vector the same length as the neighbours list in listw

listw

a listw object created for example by nb2listw; if a sequence of distance bands is to be used, it is recommended that the weights style be binary (one of c("B", "C", "U")).

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

alternative

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two.sided".

spChk

should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()

adjust.n

default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted

B1correct

default TRUE, if TRUE, the erratum referenced below: "On page 195, the coefficient of W2 in B1, (just below center of the page) should be 6, not 3." is applied; if FALSE, 3 is used (as in CrimeStat IV)

adjust.x

default TRUE, if TRUE, x values of observations with no neighbours are omitted in the denominator of G

Arc_all_x

default FALSE, if Arc_all_x=TRUE and adjust.x=TRUE, use the full x vector in part of the denominator term for G

na.action

a function (default na.fail), can also be na.omit or na.exclude - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted. na.pass is not permitted.

Author

Hisaji ONO and Roger Bivand

References

Getis. A, Ord, J. K. 1992 The analysis of spatial association by use of distance statistics, Geographical Analysis, 24, p. 195; see also Getis. A, Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716--748 tools:::Rd_expr_doi("10.1007/s11749-018-0599-x")

See Also

localG

Examples

nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79
dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100)
ndists <- length(dists)
ZG <- vector(mode="list", length=ndists)
names(ZG) <- as.character(dists)
milesxy <- cbind(nc.sids$east, nc.sids$north)
for (i in 1:ndists) {
  thisnb <- dnearneigh(milesxy, 0, dists[i])
  thislw <- nb2listw(thisnb, style="B", zero.policy=TRUE)
  ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE)
}
t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value))))
for (i in 1:ndists) {
  thisnb <- dnearneigh(milesxy, 0, dists[i])
  thislw <- nb2listw(thisnb, style="B", zero.policy=TRUE)
  ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative="two.sided")
}
t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value))))
data(oldcol)
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
res <- try(globalG.test(crime, nb2listw(COL.nb, style="B"),
 na.action=na.fail))
res
globalG.test(crime, nb2listw(COL.nb, style="B"), zero.policy=TRUE,
 na.action=na.omit)
globalG.test(crime, nb2listw(COL.nb, style="B"), zero.policy=TRUE,
 na.action=na.exclude)
try(globalG.test(crime, nb2listw(COL.nb, style="B"), na.action=na.pass))