Analysing spatial point patterns in R - CSIRO

172 Validation of fitted Gibbs models
28.1 Goodness-of-fit testing for Gibbs processes
For a fitted Gibbs process, no theory is available to support the χ 2 goodness-of-fit test or the
Kolmogorov-Smirnov test. The predicted mean number of points in a given region is not known
in closed form for a Gibbs process. Thus, the appropriate test statistic for a χ 2 test is not even
available in closed form, let alone the null distribution of this statistic.
Instead, goodness-of-fit for fitted Gibbs models often relies on the summary functions K and
G. The command envelope will accept as its first argument a fitted Gibbs model, and will
simulate from this model to determine the critical envelope.
> plot(envelope(fit, Lest, nsim = 19, global = TRUE))
envelope(fit, Lest, nsim=19, global=TRUE)
L(r)
0.00 0.05 0.10 0.15 0.20 0.25
obs
mmean
hi
lo
0.00 0.05 0.10 0.15 0.20 0.25
r
Let’s subtract the theoretical Poisson value L(r) = r to get a more readable plot:
> plot(envelope(fit, Lest, nsim = 19, global = TRUE), . - r ~ r)
envelope(fit, Lest, nsim=19, global=TRUE)
L(r) − r
−0.02 −0.01 0.00 0.01 0.02
obs
mmean
hi
lo
0.00 0.05 0.10 0.15 0.20 0.25
r
This is fairly consistent with a Strauss process.
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