[R-sig-Geo] Simple Ripley's CRS test for market point patters --- addendum.

[Rolf Turner]

I have realised that there were a couple of oversights in my previous 
posting on this issue.  One is a bit subtle; the other is a bit of a 
blunder on my part.

First the "subtle" one. The test that I proposed for CSRI is a test done 
using the estimated parameters of the proposed model to generate 
realisations of data sets under the null hypothesis.  Such tests tend to 
be conservative.  (See section 10.6.3, p. 388 ff., in [1].)

In the current instance (testing for CSRI) the conservatism can be 
overcome by simulating data conditional on the numbers of points of each 
type in the "real" data.  This can be done here via:

foo <- function(W){
s <- runifpoint(10,win=W)
m <- runifpoint(9,win=W)
l <- runifpoint(27,win=W)
superimpose(s=s,m=m,l=l)
}
simex <- expression(foo(W))

and then

set.seed(42)
E <- envelope(syn.ppp,simulate=simex,savefuns=TRUE)
dtst <- dclf.test(E)
mtst <- mad.test(E)

This gives p-values of 0.06 from the dclf test and 0.09 from the mad 
test.  Thus there appears to be some slight evidence against the null 
hypothesis.  (Evidence at the 0.10 significance level.)

That this should be so is *OBVIOUS* (!!!) if we turn to the unsubtle 
point that I overlooked.  It is clear that the pattern of ants' nests 
cannot be truly a realisation of a Poisson process since there must be a 
bit of a "hard core" effect.  Two ants' nests cannot overlap.  Thus if 
we approximate the shape of each nest by a disc, points i and j must be 
a distance of at least r_i + r_j from each other, where r_i = 
sqrt(area_i/pi), and similarly for r_j.

However I note that the data provided seem to violate this principle in 
several instances.  E.g. points 41 and 42 are a distance of only 0.2460 
metres apart but areas 41 and 42 are 12.9 and 15.2 square metres, 
yielding putative radii of 3.5917 and 3.8987 metres, whence the closest
these points could possibly be (under the "disc-shaped assumption") is
7.4904 metres, far larger than 0.2460.   So something is a bit out of 
whack here.  Perhaps these are made-up ("synthetic") data and the 
process of making up the data did not take account of the minimum 
distance constraint.

How to incorporate the "hard core" aspect of your (real?) data into the 
modelling exercise, and what the impact of it is upon your research 
question(s), is unclear to me and is likely to be complicated.

cheers,

Rolf

-- 
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

[1] Spatial Point Patterns: Methodology and Applications with R
1st Edition, Adrian Baddeley, Ege Rubak, Rolf Turner
Chapman and Hall/CRC, 2015