Some years ago, I asked how it is possible to formally assess the spatial relation between two sets of points, for instance if a building type A tends to occur close to building type B. The answer I received was extremely useful, and also provided the code to perform a simulation in R (Formally testing whether building type tends to be close to another building type?).
Now I have a related but different question:
- how to conceptualize the issue at hand from a spatial analysis perspective?
- how to build a simulation in R?
The question is: given two sets of points (A and B) in a given study region, how can I formally assess if B-points tend to cluster (i.e., tend to be close) around one (or even two, or three, for the sake of argument) of the A-points?
I am not a specialist in spatial statistic; what I conceptually came up with is:
- Equally divide the space between the A-points, e.g. making use of Thiessen polygons;
- Calculate how many B-points actually falls within each polygon centered around each A-point (let's call those polygons A-polygons);
- For each A-polygon, calculate what is the probability of observing the actual B-points count under the Null Hypothesis of a random distribution of B-points relative to the A-polygons.
While in R performing (1) and (2) is not challenging, I am stuck at (3) since I can't conceptualize the proper statistical procedure. While googling a little, I came across a statistical approach that could be relevant for my problem; the procedure is described in the help documentation of the PASSaGE program (http://www.passagesoftware.net/manual.php), which is appended here as a screenshot.