[R-sig-Geo] Cross nearest neighbor distance

[Rolf Turner]

On 06/09/11 01:13, Alper ALTINOK wrote:
>
> I appreciate for the advices, let me explain the situation a bit more with another example;
>
> Say, points are representing sampled fields for pests. Imagine you are making samplings from tomato fields to reveal possible clusters (hotspots) of pests, in a region, say 100km by 100km. Last year, you sampled 50 fields from that region, and this year 50 fields sampled. You want to compare these two years by means of cluster locations, but there is a problem; some tomato field locations are same with previous year, but some are changed to (nearby fields) due to crop-rotation, farmers' preferences etc., so these point sets do not overlap perfectly. The question is, can you compare (and comment on) pest clusters while point locations different among these point sets? (or, will it be statistically correct?)
>
> What I was hoping is, to find a way to tell, how (dis)similar the point locations of year1 and year2 are? In other words, when compared, whether the points of these two sampling sets are statistically significantly distributed against each other, or not. If not, I think comparison of two point sets will become possible. This is why I am looking for cross nearest neighor function.
>
> Well I did my best to explain the situation, hope this clarifies the issue, many thanks for the comments.

If I understand you correctly, the ``points'' of your pattern consist of 
these 50 fields.
Each year each field may be classified as having an infestation of pests 
or not.  What
this gives you is a binary random field on an irregular "grid" of 
points.  That field is evolving
over time, and is/has been observed at a number (10?) of regularly 
spaced times.

You are interested in knowing whether the locations of the ``1's'' 
(infestations) in your binary
random field (at each observation time) are dependent upon the locations 
of the 1's at the
previous observation time.

The fly in the ointment is that sometimes some of the 50 points in your 
irregular grid
change *a little bit* due to crop rotation etc.  This seems to me to be 
an aspect of the
problem that is very hard to model.  Off the top of my head I would 
approach it by
replacing any points that change by the *centroid* of their various 
manifestations.

This I think, would be a perfectly reasonable approximation provided 
that the amount
(distance) by which the points change location is *small* compared with 
distances
between genuinely distinct points.

Given that this approximation is acceptable, how can you go about 
answering the question
of interest?  You are *not* dealing with a point process, so point 
process techniques are
not of any use, although some of the machinery in spatstat would 
probably be of use in
effecting the calculations that you need to make.

I don't believe that there are any pre-programmed techniques in spatial 
statistical
analysis to handle the problem.  Others may correct me if I am wrong 
about this.
If I am correct then you will have to invent (and program up) your own 
technique.
I have a few ideas about how you might go about this, but I will refrain 
from making
any further suggestions at this time.

     cheers,

         Rolf Turner