spdep (version 0.5-74)

geary.test: Geary's C test for spatial autocorrelation

Description

Geary's test for spatial autocorrelation using a spatial weights matrix in weights list form. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of geary.mc permutations.

Usage

geary.test(x, listw, randomisation=TRUE, zero.policy=NULL,
    alternative="greater", spChk=NULL, adjust.n=TRUE)

Arguments

x

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

listw

a listw object created for example by nb2listw

randomisation

variance of I calculated under the assumption of randomisation, if FALSE normality

zero.policy

default NULL, 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

Value

• A list with class htest containing the following components:
• statistic
  the value of the standard deviate of Geary's C, in the order given in Cliff and Ord 1973, p. 21, which is (EC - C) / sqrt(VC), that is with the sign reversed with respect to the more usual (C - EC) / sqrt(VC); this means that the greater alternative for the Geary C test corresponds to the greater alternative for Moran's I test.
• p.value
  the p-value of the test.
• estimate
  the value of the observed Geary's C, its expectation and variance under the method assumption.
• alternative
  a character string describing the alternative hypothesis.
• method
  a character string giving the assumption used for calculating the standard deviate.
• data.name
  a character string giving the name(s) of the data.

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, A. D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21.

See Also

geary, geary.mc, listw2U

Examples

data(oldcol)
geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"))
geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 randomisation=FALSE)
colold.lags <- nblag(COL.nb, 3)
geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"))
geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"), alternative="greater")
print(is.symmetric.nb(COL.nb))
coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
print(is.symmetric.nb(COL.k4.nb))
geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"))
geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"),
 randomisation=FALSE)
cat("Note non-symmetric weights matrix - use listw2U()
")
geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")))
geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")), randomisation=FALSE)