Analysing spatial point patterns in R - CSIRO

198 Exploratory tools for multitype point patterns
> plot(E, main = "test of independent components")
test of independent components
K on, off(r)
0.00 0.05 0.10 0.15 0.20
obs
mmean
hi
lo
0.00 0.05 0.10 0.15 0.20 0.25
r (one unit = 662 microns)
The independence-of-components hypothesis seems to be accepted in this example.
Under the independence hypothesis,
K ij (r) = πr 2
G ij (r) = F j (r)
J ij (r) ≡ 1.
while the “i-to-any” functions have complicated values. Thus, we would normally use K ij or J ij
to construct a test statistic for independence of components.
31.4.3 Random labelling
In a randomisation test of the random labelling null hypothesis, the simulated patterns X are
generated from the dataset by holding the point locations fixed, and randomly resampling the
marks, either with replacement (independent random sampling) or without replacement (randomly
permuting the marks). The resampling operation is performed by rlabel.
Under random labelling,
J i• (r) = J(r)
K i• (r) = K(r)
G i• (r) = G(r)
(where G,K,J are the summary functions for the point process without marks) while the other,
cross-type functions have complicated values. Thus, we would normally use something like
K i• (r) − K(r) to construct a test statistic for random labelling.
To do this, cook up a little function to evaluate J i• (r) − J(r):
> Jdif