spdep (version 0.1-10)

localmoran.sad: 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

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

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.

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))