[R-sig-Geo] Moran Index n ape and spdep package

[Roger Bivand]

On Tue, 17 Jan 2017, Stefano Menichetti wrote:

> Good morning at all, I'm new on R and also I'm not so practical with spatial 
> analysis by Moran index. So, I've some practice in kriging to interpolate adn 
> before to judge by variogram effective spatial autocorrelation of my actual 
> data resolution.
> Recently I've discover Moran index that give me, it seems, a sound 
> statistical judgment about effective autocorrelation and perhaps spatial 
> continuity.
>
> I've used "ape" package to perform a Moran evaluation by simple weight  by 
> inverse distance
> library("ape")
> View(myData) (X, Y, Z attribute of pollutant concentration)
> myData.dists <- as.matrix(dist(cbind(myData$X,myData$Y)))
> myData.dists.inv <- 1/myData.dists
> diag(myData.dists.inv) <- 0
> Moran.I(myData$PCE,myData.dists.inv)
>
> Forgive my difficulties but I can not play a similar syntax with "spdep". 
> Example are not clear for me.
>
> Can you show me an example ?

library(sp)
data(meuse)
myData.dists <- as.matrix(dist(cbind(meuse$x, meuse$y)))
myData.dists.inv <- 1/myData.dists
diag(myData.dists.inv) <- 0
library("ape")
Moran.I(meuse$zinc, myData.dists.inv)

This is what you had already, and spdep can do the same, but in a much 
more flexible way, where the user has control of what is happening.

library(spdep)
nb_inf <- dnearneigh(cbind(meuse$x, meuse$y), 0, 10000)
nb_inf # dense
dists_inf <- nbdists(nb_inf, cbind(meuse$x, meuse$y))
dists_inf_inv <- lapply(dists_inf, function(x) 1/x)
lw <- nb2listw(nb_inf, glist=dists_inf_inv, style="B")
Mlw <- listw2mat(lw)
all.equal(Mlw, myData.dists.inv, check.attributes=FALSE)
Moran.I(meuse$zinc, myData.dists.inv)
Moran.I(meuse$zinc, Mlw)
moran.test(meuse$zinc, lw)

# not the same, ape::Moran.I converts to style="W" - row-standardising the 
# weights - internally and transparently

spdepI <- moran.test(meuse$zinc, nb2listw(nb_inf, glist=dists_inf_inv,
  style="W"))
apeI1 <- Moran.I(meuse$zinc, Mlw)
apeI0 <- Moran.I(meuse$zinc, myData.dists.inv)
all.equal(unname(spdepI$estimate[1]), unname(apeI0$observed))
all.equal(unname(spdepI$estimate[1]), unname(apeI1$observed))
all.equal(unname(spdepI$statistic),
  unname((apeI0$observed-apeI0$expected)/apeI0$sd))

# note that spdep::moran.test and ape::Moran.I have different defaults for 
# alternative, and that ape::Moran.I implements the randomisation variance 
# without stating that it does this

All now the same. But:

nb_tri <- tri2nb(cbind(meuse$x, meuse$y))
nb_tri # sparse
dists_tri <- nbdists(nb_tri, cbind(meuse$x, meuse$y))
dists_tri_inv <- lapply(dists_tri, function(x) 1/x)
moran.test(meuse$zinc, nb2listw(nb_tri, glist=dists_tri_inv, style="W"))

See vignette("nb") for different ways of finding neighbours. Sparse 
weights are always to be preferred over dense, because the covariance 
matrix of the observations becomes dense by inversion when spatial 
autocorrelation is present.

Moran's I can always be fooled by a wrong mean model (Moran.I and 
moran.test use the mean of the variable of interest). If there is a 
spatial trend in otherwise uncorrelated data, and the trend is not 
included in the mean model, the measure will find spurious 
autocorrelation.

Hope this clarifies,

Roger

>
> Thank you very much in advance
>
> Stefano
>
>
>
>
>
>

-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand at nhh.no
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
http://depsy.org/person/434412