localmoran.sad

0th

Percentile

Saddlepoint approximation of local Moran's Ii tests

The function implements Tiefelsdorf's application of the Saddlepoint approximation to local Moran's Ii's reference distribution. If the model object is of class "lm", global independence is assumed; if of class "sarlm", global dependence is assumed to be represented by the spatial parameter of that model. Tests are reported 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.

Keywords
spatial
Usage
localmoran.sad(model, select, nb, glist=NULL, style="W", zero.policy=NULL, alternative="greater", spChk=NULL, resfun=weighted.residuals, save.Vi=FALSE, tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001, save.M=FALSE, Omega = NULL)
"print"(x, ...) "summary"(object, ...) "print"(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=NULL)
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
save.Vi
if TRUE, return the star-shaped weights lists for each zone tested
tol
the desired accuracy (convergence tolerance) for uniroot
maxiter
the maximum number of iterations for uniroot
tol.bounds
offset from bounds for uniroot
save.M
if TRUE, save a list of left and right M products in a list for the conditional tests, or a list of the regression model matrix components
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
x
object to be printed
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.

If a histogram of the probability values of the saddlepoint estimate for the assumption of global independence is not approximately flat, the assumption is probably unjustified, and re-estimation with global dependence is recommended.

No n by n matrices are needed at any point for the test assuming no global dependence, the star-shaped weights matrices being handled as listw lists. When the test is made on residuals from a spatial regression, taking a global process into account. n by n matrices are necessary, and memory constraints may be reached for large lattices.

Value

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

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

localmoran, lm.morantest, lm.morantest.sad, errorsarlm

Aliases
  • localmoran.sad
  • listw2star
  • print.summary.localmoransad
  • summary.localmoransad
  • print.localmoransad
  • as.data.frame.localmoransad
Examples
require(maptools)
eire <- readShapePoly(system.file("etc/shapes/eire.shp", package="spdep")[1],
  ID="names", proj4string=CRS("+proj=utm +zone=30 +ellps=airy +units=km"))
eire.nb <- poly2nb(eire)
lw <- nb2listw(eire.nb)
#data(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb))
e.locmor
mean(e.locmor[,1])
sum(e.locmor[,1])/Szero(lw)
lm.morantest(e.lm, lw)
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
hist(e.locmor[,"Pr. (Sad)"])
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals))
e.locmorw1
e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent))
e.locmorw2
e.errorsar <- errorsarlm(OWNCONS ~ ROADACC, data=eire,
  listw=lw)
e.errorsar
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
Omega <- tcrossprod(invIrW(lw, rho=e.errorsar$lambda))
e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega))
e.clocmor
hist(e.clocmor[,"Pr. (Sad)"])
Documentation reproduced from package spdep, version 0.6-9, License: GPL (>= 2)

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