Spatial Autocorrelation Analysis in R

Question

I'm trying to run a spatial autocorrelation (SAC) on light values across a sampling area. I did some searching, and I've found that Moran's I (in the ape package) is a common tool used in R to do SAC. However, I ran the code and I'm not entirely sure if R is doing what I want. The code doesn't break, but I've input my variable (transformed light values) using the Moran.I function:

Moran.I (ovenbird$ARCSINE.SQRT.TRAN, ld.dist.mat)

My distance matrix (ld.dist.mat) is a matrix of distances between all points (A-O) on my grid. It looks like this:

      A     B     C     D     E     F     G     H     I     J    K     L     M     N     O
A  0.00  5.00 10.00  2.50  5.59 10.31  5.00  7.07 11.18  7.50 9.01 12.50 10.00 11.18 14.14
B  5.00  0.00  5.00  5.59  2.50  5.59 11.18  5.00 11.18  9.01 7.50  9.01 11.18 10.00 11.18
C 10.00  5.00  0.00 10.31  5.59  2.50 11.18  7.07  5.00 12.50 9.01  7.50 14.14 11.18 10.00
D  2.50  5.59 10.31  0.00  5.00 10.00  2.50  5.59 10.31  5.00 7.07 11.18  7.50  9.01 12.50
E  5.59  2.50  5.59  5.00  0.00  5.00  5.59  2.50  5.59 11.18 5.00 11.18  9.01  7.50  9.01
F 10.31  5.59  2.50 10.00  5.00  0.00 10.31  5.59  2.50 11.18 7.07  5.00 12.50 11.18  7.50
G  5.00 11.18 11.18  2.50  5.59 10.31  0.00  5.00 10.00  2.50 5.59 10.31  5.00  7.07 11.18
H  7.07  5.00  7.07  5.59  2.50  5.59  5.00  0.00  5.00  5.59 2.50  5.59 11.18  5.00 11.18
I 11.18 11.18  5.00 10.31  5.59  2.50 10.00  5.00  0.00 10.31 5.59  2.50 11.18  7.07  5.00
J  7.50  9.01 12.50  5.00 11.18 11.18  2.50  5.59 10.31  0.00 5.00 10.00  2.50  5.59 10.31
K  9.01  7.50  9.01  7.07  5.00  7.07  5.59  2.50  5.59  5.00 0.00  5.00  5.59  2.50  5.59
L 12.50  9.01  7.50 11.18 11.18  5.00 10.31  5.59  2.50 10.00 5.00  0.00 10.31  5.59  2.50
M 10.00 11.18 14.14  7.50  9.01 12.50  5.00 11.18 11.18  2.50 5.59 10.31  0.00  5.00 10.00
N 11.18 10.00 11.18  9.01  7.50 11.18  7.07  5.00  7.07  5.59 2.50  5.59  5.00  0.00  5.00
O 14.14 11.18 10.00 12.50  9.01  7.50 11.18 11.18  5.00 10.31 5.59  2.50 10.00  5.00  0.00

My question is how does R know which points on my grid are associated with each light value? I have tried print(Moran.I) to figure this out, but I have only been programming since fall of last year (2012) and I am not well versed enough in R to know how to interpret the function. Also, if R isn't identifying my light values in the right way, how do I fix that?

Any help would be greatly appreciated.

Answer 1

You can do the following to get the global and local measures of spatial autocorrelation using Moran's measure using the code below:

library(raster)
r  <-  raster(nrows=10,  ncols=10)
r[]  <-  1:ncell(r)
Moran(r) #this is the global index of autocorrelation
x1  <-  MoranLocal(r) #local measure of autocorr as a raster object that can be plotted
plot(x1) #this will plot the autocorrelation raster results

For Geary's autocorr measure:

Geary(r) #this is the global index of autocorrelation
x1  <-  GearyLocal(r) #local measure
plot(x1)