issues using Spatial autocorrelation in R at specific lags (in m) - r

Question

Since a few days I am struggling with a new challenging spatial analysis which include spatial autocorrelation in R: Specifically, I am interested in verifying the autocorrelation between points set in a grid of 50 m (more or less). My aim is to test the autocorrelation between these points (the locations where I collected the data) and to verify if the autocorrelation decreases increasing the distance among them (this is expected). My idea is to generate different radius of specific meters around each point (50 m, 100 m, 150 m and so on...) and to test the Moran's I Autocorrelation Index. Finally I would like to use ggplot to display the MI at each specific distance results (but this is easy to get once I have the MI outputs...).
My starting dataframe contains 4 coloumns: the ID of the point where data where collected, the values measured at that specific points (z) a coloumn with longitude (x) and a coloumn with latitude(y),data are displayed as follows:
#install libraries
library(sp)
library(spdep)
library(splm)
library(ape)
ID<- c(1,2,3,4,5,6)
x<-c(20.99984,20.99889, 20.99806,20.99800,20.99700,20.99732)
y<-c(52.21511,52.21489,52.21464,52.21410,52.21327,52.21278)
z<-c(1.16,0.54,0.89,0.60,1.27,1.45)
data <- data.frame(ID,x,y,z)
I read many things online and found this tutorial
https://mgimond.github.io/Spatial/spatial-autocorrelation-in-r.html#morans-i-as-a-function-of-a-distance-band
which actually shows what I'm interested in: however, it doesn't really work from the real beginning and, starting from my coordinates, I think there is a problem and I don't know how to tranform them in a proper format for R. this is the error message I get:
data <- data.frame(dataPOL$Long , dataPOL$Lat, dataPOL$Human_presence)
coordinates(data) <- c('x','y')`
proj4string(data) <- "+init=epsg:4326"
S.dist <- dnearneigh(coordinates, 0, 50) #radius of 50 meters
Error in dnearneigh(coordinates, 0, 50) : Data non-numeric

Answer 1

I did not receive any answer, but I ended up finding a solution:
I have found that the most used packages to work with spatial autocorrelation in R (in my case, Moran I) are spdep and ape.
I tried both: spdep didn't work yet but ape did. Here is the tutorial I followed for my specific case:
https://stats.idre.ucla.edu/r/faq/how-can-i-calculate-morans-i-in-r/
before calculate the Moran index, you should generate a distance matrix, I did it with the ‘rdist.earth’ from the package 'fields'.
This function measures the distance between each set of data points based on their coordinates. This function recognizes that the world is not flat, and as such calculates what are known as great-circle distances. I specified the distance in Km for my specific case.
to calculate Moran I, I ran this:
library(ape)
pop.dists.1 <- (popdists > 0 & popdists <= .06) # radius of 60m (remember
that field package works in km or miles)
Moran.I(mydataframe$myzvariable, pop.dists.1)
This is the output I got at this specific radius:
pop.dists.1 <- (popdists > 0 & popdists <= .06) #60m
Moran.I(dataPOL$Human_presence, pop.dists.1)
$observed
[1] 0.3841241 #Moran index: between -1 and 1, in here points within 60 m are
autocorrelated
$expected
[1] -0.009615385
$sd
[1] 0.08767598
$p.value
[1] 7.094019e-06
I repeated the formulas for the distances I am interested in: it works really well and increasing the distance, the Moran I index approximate 0 (which is what I expected).
I am going to plot the single outputs by using ggplot as always, in order to follow the trend of spatial autocorrelation for my z variable.
Hope this will help if needed!