lm.morantest.sad: Saddlepoint approximation of global Moran's I test

In spdep: Spatial Dependence: Weighting Schemes, Statistics

Saddlepoint approximation of global Moran's I test

Description

The function implements Tiefelsdorf's application of the Saddlepoint approximation to global Moran's I's reference distribution.

Usage

lm.morantest.sad(model, listw, zero.policy=attr(listw, "zero.policy"),
  alternative="greater", spChk=NULL, resfun=weighted.residuals,
  tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001,
  zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL)
## S3 method for class 'moransad'
print(x, ...)
## S3 method for class 'moransad'
summary(object, ...)
## S3 method for class 'summary.moransad'
print(x, ...) 

Arguments

model	an object of class lm returned by lm; weights may be specified in the lm fit, but offsets should not be used
listw	a listw object created for example by nb2listw
zero.policy	default attr(listw, "zero.policy") as set when listw was created, if attribute not set, 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
tol	the desired accuracy (convergence tolerance) for uniroot
maxiter	the maximum number of iterations for uniroot
tol.bounds	offset from bounds for uniroot
zero.tol	tolerance used to find eigenvalues close to absolute zero
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.M	return the full M matrix for use in spdep:::exactMoranAlt
save.U	return the full U matrix for use in spdep:::exactMoranAlt
x	object to be printed
object	object to be summarised
...	arguments to be passed through

Details

The function involves finding the eigenvalues of an n by n matrix, and numerically finding the root for the Saddlepoint approximation, and should therefore only be used with care when n is large.

Value

A list of class moransad with the following components:

statistic	the value of the saddlepoint approximation of the standard deviate of global Moran's I.
p.value	the p-value of the test.
estimate	the value of the observed global Moran's I.
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
internal2	f.root, iter and estim.prec from uniroot
df	degrees of freedom
tau	eigenvalues (excluding zero values)

Author(s)

Roger Bivand [e-mail]

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; 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

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)
lm.morantest(e.lm, nb2listw(eire.nb))
lm.morantest.sad(e.lm, nb2listw(eire.nb))
summary(lm.morantest.sad(e.lm, nb2listw(eire.nb)))
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent)
lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent)

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