[R-sig-Geo] How to interpret the pair correlation function?

[Adrian.Baddeley at csiro.au]

Faranak <faranakfathi at gmail.com> writes:

> I plotted a "pair correlation function" for my data as follows:
      <http://r-sig-geo.2731867.n2.nabble.com/file/n7581160/pair_correlation.jpeg> 
> It shows for r between approximately 0.3 to 0.7 the value of g(r) is greater
> than 1 which shows clustering.
> But what does that mean? How can I interpret this diagram?

g(r) > 1 for a particular value of 'r' means literally that there are more pairs of points separated by distances of approximately 'r'
in the data than would be expected for a completely random pattern.

g(r) > 1 for *all* r would suggest clustering.

Your example is not an example of clustering. 

In your example you have g(0) = 0 and g(r)  < 1 for r < 0.2,  then g(r) > 1 for r between 0.3 and 0.7. 
This is the typical behaviour of a 'soft packing'.
There are very few points found closer than a certain threshold distance (a so-called 'soft core' or 'strong inhibition' effect)
but just beyond this distance there is a tendency to find another point (a 'packing' effect). 

You should also be aware that the estimate of g(r) is computed by kernel smoothing which may have smoothed-out certain features of the curve.

It would be wise to read one of the standard books e.g.Illian et al (2008) Statistical analysis of spatial point patterns.

Adrian Baddeley
====
Prof Adrian Baddeley FAA
CSIRO Mathematics, Informatics & Statistics
Leeuwin Centre, 65 Brockway Rd, Floreat WA 6014, Australia
tel +61 8 9333 6177 skype adrian.baddeley