spdep (version 0.6-4)

localmoran: Local Moran's I statistic

Description

The local spatial statistic Moran's I is calculated for each zone based on the spatial weights object used. The values returned include a Z-value, and may be used as a diagnostic tool. The statistic is: $$I_i = \frac{(x_i-\bar{x})}{{\sum_{k=1}^{n}(x_k-\bar{x})^2}/(n-1)}{\sum_{j=1}^{n}w_{ij}(x_j-\bar{x})}$$, and its expectation and variance are given in Anselin (1995).

Usage

localmoran(x, listw, zero.policy=NULL, na.action=na.fail, 
	alternative = "greater", p.adjust.method="none", mlvar=TRUE,
        spChk=NULL)

Arguments

x

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

listw

a listw object created for example by nb2listw

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

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 ma

alternative

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

p.adjust.method

a character string specifying the probability value adjustment for multiple tests, default "none"; see p.adjustSP. Note that the number of multiple tests for each region is only taken as the number of ne

mlvar

default TRUE: values of local Moran's I are reported using the variance of the variable of interest (sum of squared deviances over n), but can be reported as the sample variance, dividing by (n-1) instead; both are used in other implementations.

spChk

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

Value

• Ii
  local moran statistic
• E.Ii
  expectation of local moran statistic
• Var.Ii
  variance of local moran statistic
• Z.Ii
  standard deviate of local moran statistic
• Pr()
  p-value of local moran statistic

Details

The values of local Moran's I are divided by the variance (or sample variance) of the variable of interest to accord with Table 1, p. 103, and formula (12), p. 99, in Anselin (1995), rathar than his formula (7), p. 98.

References

Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, 93--115; 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.

See Also

localG

Examples

data(afcon)
oid <- order(afcon$id)
resI <- localmoran(afcon$totcon, nb2listw(paper.nb))
printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),
 check.names=FALSE)
hist(resI[,5])
mean(resI[,1])
sum(resI[,1])/Szero(nb2listw(paper.nb))
moran.test(afcon$totcon, nb2listw(paper.nb))
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
resI <- localmoran(afcon$totcon, nb2listw(paper.nb),
 p.adjust.method="bonferroni")
printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),
 check.names=FALSE)
hist(resI[,5])
totcon <-afcon$totcon
is.na(totcon) <- sample(1:length(totcon), 5)
totcon
resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude,
 zero.policy=TRUE)
if (class(attr(resI.na, "na.action")) == "exclude") {
 print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2)
} else print(resI.na, digits=2)
resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb)))
print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2)