Exact global Moran's I test

The function implements Tiefelsdorf's exact global Moran's I test.

lm.morantest.exact(model, listw, zero.policy = attr(listw, "zero.policy"),
 alternative = "greater", spChk = NULL, resfun = weighted.residuals,
 zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE,
 truncErr=1e-6, zeroTreat=0.1)
# S3 method for moranex
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

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

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

a moranex object

...

arguments to be passed through

Value

A list of class moranex 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.

method

a character string giving the method used.

alternative

a character string describing the alternative hypothesis.

gamma

eigenvalues (excluding zero values)

oType

usually set to "E"

data.name

a character string giving the name(s) of the data.

df

degrees of freedom

Author

Markus Reder and Roger Bivand

References

Roger Bivand, Werner G. Müller and Markus Reder (2009) "Power calculations for global and local Moran's I." Computational Statistics & Data Analysis 53, 2859-2872.

See also

lm.morantest.sad

Examples

eire <- st_read(system.file("shapes/eire.shp", package="spData")[1])
#> Reading layer `eire' from data source 
#>   `/home/rsb/lib/r_libs/spData/shapes/eire.shp' using driver `ESRI Shapefile'
#> Simple feature collection with 26 features and 10 fields
#> Geometry type: MULTIPOLYGON
#> Dimension:     XY
#> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25
#> CRS:           NA
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)
lm.morantest(e.lm, nb2listw(eire.nb))
#> 
#> 	Global Moran I for regression residuals
#> 
#> data:  
#> model: lm(formula = OWNCONS ~ ROADACC, data = eire)
#> weights: nb2listw(eire.nb)
#> 
#> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
#> alternative hypothesis: greater
#> sample estimates:
#> Observed Moran I      Expectation         Variance 
#>       0.33660565      -0.05877741       0.01473183 
#> 
lm.morantest.sad(e.lm, nb2listw(eire.nb))
#> 
#> 	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
#> 	formula)
#> 
#> data:  
#> model:lm(formula = OWNCONS ~ ROADACC, data = eire)
#> weights: nb2listw(eire.nb)
#> 
#> Saddlepoint approximation = 2.9395, p-value = 0.001644
#> alternative hypothesis: greater
#> sample estimates:
#> Observed Moran I 
#>        0.3366057 
#> 
lm.morantest.exact(e.lm, nb2listw(eire.nb))
#> 
#> 	Global Moran I statistic with exact p-value
#> 
#> data:  
#> model:lm(formula = OWNCONS ~ ROADACC, data = eire)
#> weights: nb2listw(eire.nb)
#> 
#> Exact standard deviate = 2.9316, p-value = 0.001686
#> alternative hypothesis: greater
#> sample estimates:
#> [1] 0.3366057
#> 
lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE)
#> 
#> 	Global Moran I statistic with exact p-value
#> 
#> data:  
#> model:lm(formula = OWNCONS ~ ROADACC, data = eire)
#> weights: nb2listw(eire.nb)
#> 
#> Exact standard deviate = 2.9315, p-value = 0.001686
#> alternative hypothesis: greater
#> sample estimates:
#> [1] 0.3366057
#>