A global autocorrelation statistic for categorical data?

Hello everybody!

Sorry for the dumb question, I have very limited experience with regards to
spatial autocorrelation. I have a lot of spatial points for which I
measured both continuous and categorical variables. I need to calculate
*global* measures of spatial autocorrelation for both kinds of variables. I
know that this task is relatively easy for continuous ones, here an example
using the package elsa:

rm(list = ls())
library(raster)
library(elsa)

dta <- data.frame(Lon = (runif(60)*100),
                             Lat = (runif(60)*100),
                             Cat = sample(LETTERS[1:5], 60, replace = T),
                             Cont = (runif(60)*100))
coordinates(dta) <- ~Lon + Lat
# Moran's I global index:
moran(dta[,2], d1=0, d2=2000)
[1] -0.01694915 # The value varies given that seed was not set
# Geary's c global index:
geary(dta[,2], d1=0, d2=2000)
[1] 1
set.seed(1)
dta <- data.frame(Lon = (runif(60)*100),
                               Lat = (runif(60)*100),
                               Cat = sample(LETTERS[1:5], 60,
                                            replace = TRUE),
                               Cont = (runif(60)*100))
coordinates(dta) <- ~Lon + Lat
library(spdep)
nb <- dnearneigh(dta, 0, 50) # 2000 was far too big, all neighbours of all
moran.test(dta$Cont, nb2listw(nb, style="B"))$estimate[1]
elsa::moran(dta[,2], d1=0, d2=50)
geary.test(dta$Cont, nb2listw(nb, style="B"))$estimate[1]
elsa::geary(dta[,2], d1=0, d2=50)
joincount.multi(factor(dta$Cat), nb2listw(nb, style="B"))["Jtot",]

Jtot summarises all the k-colour matches.

Hope this clarifies,

Roger
That is, I need something like the moran or geary commands in the previous
example, but applicable to categorical covariates. I have been googleing
for a while, but I have not been able to find a solution. Any idea?

Thanks in advance!

Perep
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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
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en

A global autocorrelation statistic for categorical data?

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