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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:

  1. Equally divide the space between the A-points, e.g. making use of Thiessen polygons;
  2. Calculate how many B-points actually falls within each polygon centered around each A-point (let's call those polygons A-polygons);
  3. 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.

enter image description here

closed as too broad by PolyGeo Feb 21 '18 at 7:56

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • You seem to be asking three questions even though two were unmarked in your original question. – PolyGeo Jan 7 '18 at 20:44
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    I don't understand how these questions go beyond the thread you reference: what's new about them and what isn't answered there? – whuber Jan 10 '18 at 22:05
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For question 3, couldn't you create a set of random points, generate your thiessen polygons and run the analysis on these. You could repeat this n-times and average your results. This could be used as your null hypothesis.

Is there any reason why you need to divide things up into polygons? By using thiessen polygons, you are likely to miss out points that are close to each other in some cases. It would be good to clarify why you want to go this route. You could instead look at density of points within a set radius? Or make an inverse distance index such as the sum of the inverse distances of points B to each point in A (as an example).

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