spdep: localmoran.exact – R documentation

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localmoran.exact

Exact local Moran's Ii tests

Description

localmoran.exact provides exact local Moran's Ii tests under the null hypothesis, while localmoran.exact.alt provides exact local Moran's Ii tests under the alternative hypothesis. In this case, the model may be a fitted model derived from a model fitted by spatialreg::errorsarlm, with the covariance matrix can be passed through the Omega= argument.

Usage

localmoran.exact(model, select, nb, glist = NULL, style = "W", 
 zero.policy = NULL, alternative = "greater", spChk = NULL, 
 resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6, 
 zeroTreat=0.1)
localmoran.exact.alt(model, select, nb, glist = NULL, style = "W",
 zero.policy = NULL, alternative = "greater", spChk = NULL,
 resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE,
 save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1)
## S3 method for class 'localmoranex'
print(x, ...)
## S3 method for class 'localmoranex'
as.data.frame(x, row.names=NULL, optional=FALSE, ...)

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`
`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.Vi`	if TRUE, return the star-shaped weights lists for each zone tested
`save.M`	if TRUE, save a list of left and right M products
`useTP`	default FALSE, if TRUE, use truncation point in integration rather than upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69
`truncErr`	when useTP=TRUE, pass truncation error to truncation point function
`zeroTreat`	when useTP=TRUE, pass zero adjustment to truncation point function
`x`	object to be printed
`row.names`	ignored argument to `as.data.frame.localmoranex`; row names assigned from localmoranex object
`optional`	ignored argument to `as.data.frame.localmoranex`; row names assigned from localmoranex object
`...`	arguments to be passed through

Value

A list with class localmoranex containing "select" lists, each with class moranex with the following components:

`statistic`	the value of the exact standard deviate of global Moran's I.
`p.value`	the p-value of the test.
`estimate`	the value of the observed local Moran's Ii.
`method`	a character string giving the method used.
`alternative`	a character string describing the alternative hypothesis.
`gamma`	eigenvalues (two extreme values for null, vector for alternative)
`oType`	usually set to "E", but set to "N" if the integration leads to an out of domain value for `qnorm`, when the Normal assumption is substituted. This only occurs when the output p-value would be very close to zero
`data.name`	a character string giving the name(s) of the data.
`df`	degrees of freedom
`i`	zone tested
`Vi`	zone tested

When the alternative is being tested, a list of left and right M products in attribute M.

Author(s)

Markus Reder and Roger Bivand

References

Bivand RS, Müller W, Reder M (2009) Power calculations for global and local Moran’s I. Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi: 10.1007/s11749-018-0599-x

Examples

eire <- st_read(system.file("shapes/eire.shp", package="spData")[1])
row.names(eire) <- as.character(eire$names)
st_crs(eire) <- "+proj=utm +zone=30 +ellps=airy +units=km"
eire.nb <- poly2nb(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
localmoran.sad(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE)
run <- FALSE
if (requireNamespace("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,
 listw=nb2listw(eire.nb))
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
localmoran.exact.alt(lm.target, nb=eire.nb)
}
if (run) {
Omega <- invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda)
Omega1 <- tcrossprod(Omega)
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1)
}
if (run) {
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE)
}

spdep

Spatial Dependence: Weighting Schemes, Statistics

v1.1-11

GPL (>= 2)

Authors

Roger Bivand [cre, aut] (<https://orcid.org/0000-0003-2392-6140>), Micah Altman [ctb], Luc Anselin [ctb], Renato Assunção [ctb], Olaf Berke [ctb], Andrew Bernat [ctb], Guillaume Blanchet [ctb], Eric Blankmeyer [ctb], Marilia Carvalho [ctb], Bjarke Christensen [ctb], Yongwan Chun [ctb], Carsten Dormann [ctb], Stéphane Dray [ctb], Virgilio Gómez-Rubio [ctb], Martin Gubri [ctb], Rein Halbersma [ctb], Elias Krainski [ctb], Pierre Legendre [ctb], Nicholas Lewin-Koh [ctb], Angela Li [ctb], Hongfei Li [ctb], Jielai Ma [ctb], Abhirup Mallik [ctb, trl], Giovanni Millo [ctb], Werner Mueller [ctb], Hisaji Ono [ctb], Pedro Peres-Neto [ctb], Gianfranco Piras [ctb], Markus Reder [ctb], Jeff Sauer [ctb], Michael Tiefelsdorf [ctb], René Westerholt [ctb], Levi Wolf [ctb], Danlin Yu [ctb]

Initial release

2021-09-07