Implementing and interpreting join count analysis with spdep

On Tue, 7 Feb 2017, Justin Schuetz wrote:

> 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)

At this point you are probably deciding the outcome of the tests -
different weights will give different outcomes. The fewer neighbours the
better is a good rule, otherwise the relationships may be heavily
smoothed. See vignette("nb").

>
> 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

It is also possible to use joincount.multi() to compare all with all (here
1-1, 1-2, 1-3, 2-2, 2-3, 3-3), rather than 1 with not-1 and so on. Also
look at alternative=, as your 3-3 looks close to significant negative
autocorrelation (for your preferred weights).

Roger

>
> 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.
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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
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
http://depsy.org/person/444584