# geary.test

0th

Percentile

##### Geary's C test for spatial autocorrelation

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.

Keywords
spatial
##### 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()
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:

##### Note

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, listw2U() can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative (thanks to Franz Munoz I for a well documented bug report). Geary's C is affected by non-symmetric weights under normality much more than Moran's I. From 0.4-35, the sign of the standard deviate of C is changed to match Cliff and Ord (1973, p. 21).

##### 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.

• geary.test
##### 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()\n")
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)
Documentation reproduced from package spdep, version 0.6-9, License: GPL (>= 2)

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