lm.morantest.sad: Saddlepoint approximation of global Moran's I test
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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

lm.morantest.sad(model, listw, zero.policy=NULL, 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, ...)

`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 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`
`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

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.

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)

Roger Bivand Roger.Bivand@nhh.no

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.

lm.morantest

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)
#data(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)