localmoran.sad {spdep}R Documentation

Saddlepoint approximation of local Moran's Ii tests

Description

The function implements Tiefelsdorf's application of the Saddlepoint approximation to local Moran's Ii's reference distribution. Tests are reported for separately for each zone selected, and may be summarised using summary.localmoransad. Values of local Moran's Ii agree with those from localmoran(), but in that function, the standard deviate - here the Saddlepoint approximation - is based on the randomisation assumption.

Usage

localmoran.sad(model, select, nb, glist=NULL, style="W", zero.policy=FALSE,
  alternative="greater", spChk=NULL, save.Vi=FALSE)
as.data.frame.localmoransad(x, row.names=NULL, optional=FALSE) 
print.localmoransad(x, ...)
summary.localmoransad(object, ...)
print.summary.localmoransad(x, ...)
listw2star(listw, ireg, style, n, D, a, zero.policy=FALSE)

Arguments

model an object of class lm returned by lm; weights and offsets should not be used
select an integer vector of the id. numbers of zones to be tested
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 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()
save.Vi if TRUE, return the star-shaped weights lists for each zone tested
x object to be printed
row.names ignored argument to as.data.frame.localmoransad; row names assigned from localmoransad object
optional ignored argument to as.data.frame.localmoransad; row names assigned from localmoransad object
object object to be summarised
... arguments to be passed through
listw a listw object created for example by nb2listw
ireg a zone number
n internal value depending on listw and style
D internal value depending on listw and style
a internal value depending on listw and style

Details

The function implements the analytical eigenvalue calculation together with trace shortcuts given or suggested in Tiefelsdorf (2002), partly following remarks by J. Keith Ord, and uses the Saddlepoint analytical solution from Tiefelsdorf's SPSS code. No n by n matrices are needed at any point, the star-shaped weights matrices being handled as listw lists.

Value

A list with class localmoransad containing "select" lists, each with class moransad with the following components:

statistic the value of the saddlepoint approximation of the standard deviate of local Moran's Ii.
p.value the p-value of the test.
estimate the value of the observed local Moran's Ii.
alternative a character string describing the alternative hypothesis.
method a character string giving the method used.
data.name a character string giving the name(s) of the data.
internal1 Saddlepoint omega, r and u
df degrees of freedom
tau maximum and minimum analytical eigenvalues
i zone tested

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206; see also Tiefelsdorf's SPSS code: http://geog-www.sbs.ohio-state.edu/faculty/tiefelsdorf/GeoStat.htm.

See Also

localmoran, lm.morantest, lm.morantest.sad

Examples

data(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire.df)
e.locmor <- summary(localmoran.sad(e.lm, eire.nb, select=1:nrow(eire.df)))
mean(e.locmor[,1])
lm.morantest(e.lm, nb2listw(eire.nb))

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