localmoran.exact: Exact local Moran's Ii tests

In spdep: Spatial Dependence: Weighting Schemes, Statistics

Exact local Moran's Ii tests

Description

localmoran.exact provides exact local Moran's Ii tests under the null hypothesis, while localmoran.exact.alt provides exact local Moran's Ii tests under the alternative hypothesis. In this case, the model may be a fitted model derived from a model fitted by spatialreg::errorsarlm, with the covariance matrix can be passed through the Omega= argument.

Usage

localmoran.exact(model, select, nb, glist = NULL, style = "W", 
 zero.policy = NULL, alternative = "two.sided", spChk = NULL, 
 resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6, 
 zeroTreat=0.1)
localmoran.exact.alt(model, select, nb, glist = NULL, style = "W",
 zero.policy = NULL, alternative = "two.sided", spChk = NULL,
 resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE,
 save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1)
## S3 method for class 'localmoranex'
print(x, ...)
## S3 method for class 'localmoranex'
as.data.frame(x, row.names=NULL, optional=FALSE, ...)

Arguments

model	an object of class lm returned by lm (assuming no global spatial autocorrelation), or an object of class sarlm returned by a spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented by the model spatial coefficient); weights may be specified in the lm fit, but offsets should not be used
select	an integer vector of the id. numbers of zones to be tested; if missing, all zones
nb	a list of neighbours of class nb
glist	a list of general weights corresponding to neighbours
style	can take values W, B, C, and S
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()
resfun	default: weighted.residuals; the function to be used to extract residuals from the lm object, may be residuals, weighted.residuals, rstandard, or rstudent
Omega	A SAR process matrix may be passed in to test an alternative hypothesis, for example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() is taken internally
save.Vi	if TRUE, return the star-shaped weights lists for each zone tested
save.M	if TRUE, save a list of left and right M products
useTP	default FALSE, if TRUE, use truncation point in integration rather than upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69
truncErr	when useTP=TRUE, pass truncation error to truncation point function
zeroTreat	when useTP=TRUE, pass zero adjustment to truncation point function
x	object to be printed
row.names	ignored argument to as.data.frame.localmoranex; row names assigned from localmoranex object
optional	ignored argument to as.data.frame.localmoranex; row names assigned from localmoranex object
...	arguments to be passed through

Value

A list with class localmoranex containing "select" lists, each with class moranex with the following components:

statistic	the value of the exact standard deviate of global Moran's I.
p.value	the p-value of the test.
estimate	the value of the observed local Moran's Ii.
method	a character string giving the method used.
alternative	a character string describing the alternative hypothesis.
gamma	eigenvalues (two extreme values for null, vector for alternative)
oType	usually set to "E", but set to "N" if the integration leads to an out of domain value for qnorm, when the Normal assumption is substituted. This only occurs when the output p-value would be very close to zero
data.name	a character string giving the name(s) of the data.
df	degrees of freedom
i	zone tested
Vi	zone tested

When the alternative is being tested, a list of left and right M products in attribute M.

Author(s)

Markus Reder and Roger Bivand

References

Bivand RS, Müller W, Reder M (2009) Power calculations for global and local Moran’s I. Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-018-0599-x")}

See Also

lm.morantest.exact, localmoran.sad

Examples

eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
localmoran.sad(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE)
run <- FALSE
if (requireNamespace("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,
 listw=nb2listw(eire.nb))
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
localmoran.exact.alt(lm.target, nb=eire.nb)
}
if (run) {
Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda)
Omega1 <- tcrossprod(Omega)
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1)
}
if (run) {
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE)
}

spdep documentation built on Sept. 13, 2024, 5:07 p.m.