How to test spatial correlation between two point layers

Question

I have two point layers, which visually have spatial correlation. I'd like to test it but wonder if there is such a method or index？

Answer 1

Since your point pattern is serial in nature, I would recommend a Kulldorff Spatial Scan Statistic using a Bernoulli model. This is a type of point pattern statistic that does not assume an homogenious point process and is inherently multiscale.

Sorry to say that this is not available in ArcGIS. Fortunately, the software SatScan has Binomial and Poisson likelihood scan statistics available (and is even GUI driven).

If you would like to go the R route take a look at the "kulldorff" function in the "SpatialEpi" package.

Answer 2

You could buffer out within a distance range, using different ranges and then factor the results for changes in buffer distance to establish the degree of correlation factor, for addressing points you could try the same as well as join table for matching addresses and find factors for address accuracy matches at changes over distance range factors.

Answer 3

If the points from two layers are coincident and you are interested in the correlation of two (or more) different variables for this set of points you could try lisa.nc function from ncf R package. According to manual:

lisa.nc is a function to estimate the (noncentred) local indicators of spatial association. The function requires multiple observations at each location.

This will give you LISA indicators (here is a reference for the method) and their significance for high-high, low-low, high-low and low-high patterns among your observations. Use plot.lisa for quick visual inspection of results.

Here is an example from manual:

#first generate some sample data
x <- expand.grid(1:20, 1:5)[,1]
y <- expand.grid(1:20, 1:5)[,2]
#z data from an exponential random field
z <- cbind(
rmvn.spa(x=x, y=y, p=2, method="exp"),
rmvn.spa(x=x, y=y, p=2, method="exp")
)
#lisa.nc analysis
fit1 <- lisa.nc(x=x, y=y, z=z, neigh=3)
plot.lisa(fit1)