[R-sig-Geo] Implementing and interpreting join count analysis with spdep

[Justin Schuetz]

List members,

I am trying to assess whether points of the same color are spatially autocorrelated. I have limited familiarity with spdep and join count analyses and would like to confirm that I am implementing and interpreting the analysis correctly. Below is a summary of the data, code used in the analysis, results, and my quick interpretation. If someone familiar with this type of analysis (or alternatives that are better able to address the question) could offer feedback, I would greatly appreciate it...particularly if you can help me understand how best to choose the style parameter in nb2listw function.

Many thanks,

Justin

##### POINT DATA

my.points
# A tibble: 50 × 4
   SVSPP JGS.UTM.X JGS.UTM.Y JGS.COLOR
   <int>     <dbl>     <dbl>     <int>
1     13 -14272.27   4035288         3
2     15 265382.54   4398047         3
3     22 552678.02   4537646         3
4     23 430904.66   4524648         3
5     24 -43587.79   4050674         3
6     25  67560.06   4190581         3
7     26 326773.57   4488521         3
8     27 578645.44   4735815         3
9     28 533183.23   4722559         3
10    33 368053.13   4566608         3
# ... with 40 more rows

##### CODE

# make SpatialPoints object and specify projection

coords <- my.points[, c("JGS.UTM.X", "JGS.UTM.Y")] 
UTM19N <- "+proj=utm +zone=19 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"
lat.lon <- SpatialPoints(coords, CRS(UTM19N)) 

# generate spatial weights matrix (inverse distance weighting among all points)

my.k.neighbors <- knearneigh(lat.lon, k = length(lat.lon) - 1, longlat = FALSE)
my.neighbors <- knn2nb(my.k.neighbors)
my.distances <- nbdists(my.neighbors, lat.lon)
my.weights <- lapply(my.distances, function(x) 1/(x))
my.list <- nb2listw(my.neighbors, glist = my.weights, style = "S")

# identify colors

my.colors <- as.factor(my.points$JGS.COLOR)

# assess whether similar colors are closer to each other than expected by chance
# given fixed point locations

joincount.mc(my.colors, my.list, nsim = 1000)

##### RESULTS

	Monte-Carlo simulation of join-count statistic

data:  my.colors 
weights: my.list 
number of simulations + 1: 1001 

Join-count statistic for 1 = 0.2037, rank of observed statistic = 987, p-value = 0.01399
alternative hypothesis: greater
sample estimates:
    mean of simulation variance of simulation 
           0.061423025            0.001758675 


	Monte-Carlo simulation of join-count statistic

data:  my.colors 
weights: my.list 
number of simulations + 1: 1001 

Join-count statistic for 2 = 0.076401, rank of observed statistic = 754, p-value = 0.2468
alternative hypothesis: greater
sample estimates:
    mean of simulation variance of simulation 
           0.060196719            0.001639431 


	Monte-Carlo simulation of join-count statistic

data:  my.colors 
weights: my.list 
number of simulations + 1: 1001 

Join-count statistic for 3 = 19.002, rank of observed statistic = 36, p-value = 0.964
alternative hypothesis: greater
sample estimates:
    mean of simulation variance of simulation 
            19.3165692              0.0451797 

##### INTERPRETATION

Points with color "1" are closer to each other than expected by chance, whereas there is 
little evidence that points with colors "2" (or "3") are spatially autocorrelated.