[R-sig-Geo] pair correlation function - changes btw 2005-2009?

[Friderike Oehler]

Dear Adrian,

Thank you very much for your thorough answer of my question. In fact, the
observation window and x-/y-coordinates were the same in 2005 and 2009. I
did specify the r parameter in 2009, which was not possible in early 2005.
Using the default r value does not permit to see the peak in the function at
250, because the limit is set to r=200, it thus seems that there is the same
shift of the peak compared to the 2005 plot.

Thank you also for confirming that the new plot should be the correct one.
It is evident that the inter-point distance of 250 occurs very frequently in
the pattern, yes. 

After all, many, many thanks for your continued active development of the
pcf-function and the whole spatstat package which is of great value.

Friderike



-----Original Message-----
From: Adrian.Baddeley at csiro.au [mailto:Adrian.Baddeley at csiro.au] 
Sent: 10 August 2009 04:53
To: r-sig-geo at stat.math.ethz.ch
Cc: friderike.oehler at jrc.ec.europa.eu; r.turner at auckland.ac.nz
Subject: pair correlation function - changes btw 2005-2009?

"Friderike Oehler" writes:

> I am still struggling with the pcf (spatstat package):
> I try to reproduce a plot that I did in 2005 using exactly the same 
> point pattern (a small sample of 18 points, extremely clustered) and 
> the same pcf-parameters:
> kernel="epanechnikov", stoyan=0.15, correction="Ripley" (code see below).

> However there is a shift on the r-axis in my present plot against the 
> one from 2005: The form of the curve is the same, but while in 2005 I 
> had one prominent peak at about r=135, the same peak is now located at
approx.
> r=250. Also, in the earlier plot, g(r)=1 was reached at abour r=20, 
> now at r=55.



> I checked the FAQs and Latest releases page at 
> http://www.spatstat.org/spatstat/, but could not find what could cause 
> this different behaviour of the function. Is is anyway possible that a 
> change in the code of the function since 2005 causes the observed 
> differences? If not, what else could it be?

Yes, the code for 'pcf' has certainly changed since 2005. A lot of related
code in 'R' (such as the code in density.default that is used by pcf.ppp)
has also changed since 2005.



First, please check that the window for the point pattern (as well as the x
and y coordinates) is exactly the same as the one you used in 2005. The
choice of window affects the edge corrections and hence the final result.



If that's not the problem, then the most plausible scenario is the
following.

To perform the analysis described above, you had to override some of the
defaults in pcf.ppp, in particular, the default maximum value of 'r'. The
default is there because it is known in the literature that the standard
edge corrections can introduce large bias and variance when r is large.



Since the data are extremely clustered, the most plausible explanation is
that the software changes between 2005 and 2009 (which were mostly BUG
FIXES) , together with the extreme clustering, have caused the discrepancy
in output.



The current output from pcf.ppp in spatstat 1.16-1 looks correct to me. If
you look at

     hist(pairdist(ab2))

it's clear that there is a mode of pairwise distances at about r=250. This
is also reflected in

    plot(Kest(ab2, r=seq(0,400,2.5)),xlim=c(0,400))

which shows a steep jump in the empirical K function at about r=250. So the
blip in the pcf at r=250 is real and correct.



Thus, if there was a discrepancy, it seems likely that the current code is
correct and the 2005 code contained a bug that cuased the discrepancy.



A summary of the change history of pcf.ppp is listed below. It was
introduced in spatstat 1.6-4 (April 2005). The argument 'r' was introduced
in spatstat 1.7-13 (October 2005). A completely new, faster algorithm for
computing pairwise distances was implemented in spatstat 1.9-2 (June 2006)
along with a change to the default rule for the maximum value of 'r'.  The
default value of the x limits for plotting was changed in spatstat 1.9-3
(June 2006). The smoothing algorithm was changed to use the new R function
density.default in spatstat 1.11-0. The C routine was modified in spatstat
1.13-0. There were cosmetic changes in spatstat 1.10-0, 1.11-1, 1.12-2,
1.15-2 and 1.16-1.



regards

Adrian Baddeley