Computes simulation envelopes of a summary function for a three-dimensional point pattern.
# S3 method for pp3
envelope(Y, fun=K3est, nsim=99, nrank=1, ...,
funargs=list(), funYargs=funargs, simulate=NULL, verbose=TRUE,
transform=NULL,global=FALSE,ginterval=NULL,use.theory=NULL,
alternative=c("two.sided", "less", "greater"),
scale=NULL, clamp=FALSE,
savefuns=FALSE, savepatterns=FALSE,
nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL,
maxnerr=nsim, rejectNA=FALSE, silent=FALSE,
do.pwrong=FALSE, envir.simul=NULL)A function value table (object of class "fv")
which can be plotted directly.
See envelope for further details.
The envelope command performs simulations and
computes envelopes of a summary statistic based on the simulations.
The result is an object that can be plotted to display the envelopes.
The envelopes can be used to assess the goodness-of-fit of
a point process model to point pattern data.
The envelope function is generic, with methods for
the classes "ppp", "ppm" and "kppm"
described in the help file for envelope.
This function envelope.pp3 is the method for
three-dimensional point patterns (objects of class "pp3").
For the most basic use, if you have a 3D point pattern X and
you want to test Complete Spatial Randomness (CSR), type
plot(envelope(X, K3est,nsim=39)) to see the three-dimensional
\(K\) function for X plotted together with the envelopes of
the three-dimensional \(K\) function for 39 simulations of CSR.
To create simulation envelopes, the command envelope(Y, ...)
first generates nsim random point patterns
in one of the following ways.
If simulate=NULL,
then we generate nsim simulations of
Complete Spatial Randomness (i.e. nsim simulated point patterns
each being a realisation of the uniform Poisson point process)
with the same intensity as the pattern Y.
If simulate is supplied, then it determines how the
simulated point patterns are generated.
See envelope for details.
The summary statistic fun is applied to each of these simulated
patterns. Typically fun is one of the functions
K3est, G3est, F3est or pcf3est.
It may also be a character string
containing the name of one of these functions.
For further information, see the documentation for
envelope.
Baddeley, A.J, Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42, 641--668.
pp3,
rpoispp3,
K3est,
G3est,
F3est,
pcf3est.
X <- rpoispp3(20, box3())
if(interactive()) {
plot(envelope(X, nsim=39))
}
# \testonly{
plot(envelope(X, nsim=4))
# }
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