Implementing and interpreting join count analysis with spdep

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.