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
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