Analysing spatial point patterns in R - CSIRO

31.4 Randomisation tests 197
31.4 Randomisation tests
Simulation envelopes of summary functions can be used to test various null hypotheses for
marked point patterns.
31.4.1 Poisson null
The null hypothesis of a homogeneous Poisson marked point process can be tested by direct
simulation, using envelope as before. For example, using the cross-type K function as the test
statistic,
> data(amacrine)
> E plot(E, main = "test of marked Poisson model")
test of marked Poisson model
K on, off(r)
0.00 0.05 0.10 0.15 0.20
obs
theo
hi
lo
0.00 0.05 0.10 0.15 0.20 0.25
r (one unit = 662 microns)
Notice that the arguments i and j here do not match any of the formal arguments of
envelope, so they are passed toKcross. This has the effect of callingKcross(X, i="on", j="off")
for each of the simulated point patterns X. Each simulated pattern is generated by the homogeneous
Poisson point process with intensities estimated from the dataset amacrine.
31.4.2 Independence of components
It’s also possible to test other null hypotheses by a randomisation test. We discussed two popular
null hypotheses:
random labelling: given the locations X, the marks are conditionally independent and
identically distributed;
independence of components: the sub-processes X m of points of each mark m, are independent
point processes.
In a randomisation test of the independence-of-components hypothesis, the simulated patterns
X are generated from the dataset by splitting the data into sub-patterns of points of one
type, and randomly shifting these sub-patterns, independently of each other. The shifting is
performed by rshift:
> E