[R-sig-Geo] question on raster Moran's I statistical significance

[Roger Bivand]

On Wed, 20 Oct 2021, Gabriel Cotlier wrote:

> Hello,
>
> I would like to estimate the Moran's *I* coefficient for raster data and
> together with the statical significance of the spatial autocorrelation
> obtained.
>
> I found that the raster package function Moran() although calculates the
> spatial autocorrelation index it apparently does not give directly the
> statical significance of the results obtained :
> https://search.r-project.org/CRAN/refmans/raster/html/autocor.html
>
> Could it be be possible to obtain the statistical significance of the
> results with either raster package or similar one?

fortunes::fortune("This is R")


library(raster)
r <- raster(nrows=10, ncols=10)
values(r) <- 1:ncell(r)
f <- matrix(c(0,1,0,1,0,1,0,1,0), nrow=3)
(rI <- Moran(r, f))
r1 <- r
nsim <- 499
res <- numeric(nsim)
set.seed(1)
for (i in 1:nsim) {
   values(r1) <- values(r)[sample(prod(dim(r)))]
   res[i] <- Moran(r1, f)
}

Hope-type tests date back to Cliff and Ord; they are permutation 
bootstraps.

r_g <- as(r, "SpatialPixelsDataFrame")
library(spdep)
nb <- poly2nb(as(r_g, "SpatialPolygons"), queen=FALSE)
set.seed(1)
o <- moran.mc(r_g$layer, nb2listw(nb, style="B"), nsim=nsim,
   return_boot=TRUE)
x_a <- range(c(o$t, o$t0, res, rI))
plot(density(o$t), xlim=x_a)
abline(v=o$t0)
lines(density(res), lty=2)
abline(v=rI, lty=2)

It is not immediately obvious from the code of raster::Moran() why it is 
different, possibly because of padding the edges of the raster and 
thus increasing the cell count.

For added speed, the bootstrap can be parallelized in both cases; polygon 
boundaries are perhaps not ideal.

Hope this clarifies. Always provide a reproducible example, never post 
HTML mail.

Roger Bivand

>
> Thanks a lot.
> Kind regards,
> Gabriel
>
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>
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-- 
Roger Bivand
Emeritus Professor
Department of Economics, Norwegian School of Economics,
Postboks 3490 Ytre Sandviken, 5045 Bergen, Norway.
e-mail: Roger.Bivand using nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en