On Thu, 21 Oct 2021, Gabriel Cotlier wrote:
Hello
Thank you very much.
I have large raster layers and would like to ask, in order to reduce the
processing time of the simulation, choosing a smaller nsim value could help
? and if so, what could be the minimum nsim value recommended?
If you examine the code, you see that raster::Moran() always performs
multiple raster::focal() calls, effectively constructing the spatial
weights on each run. The problem is not nsim, it is the way that
raster::Moran() is constructed.
Indeed, using a Hope-type test gives the same inferential outcome as using
asymptotic methods for global tests for spatial autocorrelation, and is
superfluous, but no other approach is feasible for raster::Moran() (which
by the way only seems to use 4 neighbours although claiming it uses 8).
1. How large is large?
It is possible to generate nb neighbour objects for large data sets,
making the use of spdep::moran.test() feasible, certainly for tens of
thousands of observations (all the census tracts in coterminous US, for
example).
This uses distances between raster cell centres to find neighbours:
library(spdep)
Loading required package: sp
Loading required package: spData
Loading required package: sf
Linking to GEOS 3.10.0, GDAL 3.3.2, PROJ 8.1.1
crds <- expand.grid(x=1:800, y=1:1200)
dim(crds)
[1] 960000 2
grd <- st_as_sf(crds, coords=c("x", "y"))
grd$z <- runif(nrow(grd))
system.time(dnbr <- dnearneigh(grd, 0, 1.01))
user system elapsed
30.065 0.235 30.381
dnbr
Neighbour list object:
Number of regions: 960000
Number of nonzero links: 3836000
Percentage nonzero weights: 0.0004162326
Average number of links: 3.995833
system.time(dnbq <- dnearneigh(grd, 0, 1.42))
user system elapsed
54.502 0.080 54.699
dnbq
Neighbour list object:
Number of regions: 960000
Number of nonzero links: 7668004
Percentage nonzero weights: 0.0008320317
Average number of links: 7.987504
Once the neighbour objects are ready, conversion to spatial weights
objects takes some time, and computing I with a constant mean model
depends on the numbers of neighbours:
system.time(lwr <- nb2listw(dnbr, style="B"))
user system elapsed
6.694 0.000 6.722
system.time(Ir <- moran.test(grd$z, lwr))
user system elapsed
24.371 0.000 24.470
Ir
Moran I test under randomisation
data: grd$z
weights: lwr
Moran I statistic standard deviate = -0.06337, p-value = 0.5253
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
-4.679899e-05 -1.041668e-06 5.213749e-07
system.time(lwq <- nb2listw(dnbq, style="B"))
user system elapsed
6.804 0.000 6.828
system.time(Iq <- moran.test(grd$z, lwq))
user system elapsed
46.703 0.012 46.843
Iq
Moran I test under randomisation
data: grd$z
weights: lwq
Moran I statistic standard deviate = -0.70373, p-value = 0.7592
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
-3.604417e-04 -1.041668e-06 2.608222e-07
2. The larger your N, the less likely that the test means anything at all,
because the assumption is that the observed entities are not simply
arbitrary products of, say, resolution.
If you think of global Moran's I as a specification test of a regression
of the variable of interest on the constant (the mean model is just the
constant), for raster data the resolution controls the outcome
(downscaling/upscaling will shift Moran's I). If you include covariates,
patterning in the residuals of a richer model may well abate.
Hope this clarifies,
Roger
Thanks a lot again.
Kind regards,
On Wed, Oct 20, 2021 at 8:45 PM Roger Bivand <roger.biv...@nhh.no> wrote:
On Wed, 20 Oct 2021, Gabriel Cotlier wrote:
Hello,
I would like to estimate the Moran's *I* coefficient for raster data and
together with the statical significance of the spatial autocorrelation
obtained.
I found that the raster package function Moran() although calculates the
spatial autocorrelation index it apparently does not give directly the
statical significance of the results obtained :
https://search.r-project.org/CRAN/refmans/raster/html/autocor.html
Could it be be possible to obtain the statistical significance of the
results with either raster package or similar one?
fortunes::fortune("This is R")
library(raster)
r <- raster(nrows=10, ncols=10)
values(r) <- 1:ncell(r)
f <- matrix(c(0,1,0,1,0,1,0,1,0), nrow=3)
(rI <- Moran(r, f))
r1 <- r
nsim <- 499
res <- numeric(nsim)
set.seed(1)
for (i in 1:nsim) {
values(r1) <- values(r)[sample(prod(dim(r)))]
res[i] <- Moran(r1, f)
}
Hope-type tests date back to Cliff and Ord; they are permutation
bootstraps.
r_g <- as(r, "SpatialPixelsDataFrame")
library(spdep)
nb <- poly2nb(as(r_g, "SpatialPolygons"), queen=FALSE)
set.seed(1)
o <- moran.mc(r_g$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
[[alternative HTML version deleted]]
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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.biv...@nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
--
Roger Bivand
Emeritus Professor
Department of Economics, Norwegian School of Economics,
Postboks 3490 Ytre Sandviken, 5045 Bergen, Norway.
e-mail: roger.biv...@nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
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