envelope.pp3
Simulation Envelopes of Summary Function for 3D Point Pattern
Computes simulation envelopes of a summary function for a three-dimensional point pattern.
Usage
# 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)
Arguments
- Y
A three-dimensional point pattern (object of class
"pp3"
).- fun
Function that computes the desired summary statistic for a 3D point pattern.
- nsim
Number of simulated point patterns to be generated when computing the envelopes.
- nrank
Integer. Rank of the envelope value amongst the
nsim
simulated values. A rank of 1 means that the minimum and maximum simulated values will be used.- …
Extra arguments passed to
fun
.- funargs
A list, containing extra arguments to be passed to
fun
.- funYargs
Optional. A list, containing extra arguments to be passed to
fun
when applied to the original dataY
only.- simulate
Optional. Specifies how to generate the simulated point patterns. If
simulate
is an expression in the R language, then this expression will be evaluatednsim
times, to obtainnsim
point patterns which are taken as the simulated patterns from which the envelopes are computed. Ifsimulate
is a function, then this function will be repeatedly applied to the data patternY
to obtainnsim
simulated patterns. Ifsimulate
is a list of point patterns, then the entries in this list will be treated as the simulated patterns from which the envelopes are computed. Alternativelysimulate
may be an object produced by theenvelope
command: see Details.- verbose
Logical flag indicating whether to print progress reports during the simulations.
- transform
Optional. A transformation to be applied to the function values, before the envelopes are computed. An expression object (see Details).
- global
Logical flag indicating whether envelopes should be pointwise (
global=FALSE
) or simultaneous (global=TRUE
).- ginterval
Optional. A vector of length 2 specifying the interval of \(r\) values for the simultaneous critical envelopes. Only relevant if
global=TRUE
.- use.theory
Logical value indicating whether to use the theoretical value, computed by
fun
, as the reference value for simultaneous envelopes. Applicable only whenglobal=TRUE
.- alternative
Character string determining whether the envelope corresponds to a two-sided test (
side="two.sided"
, the default) or a one-sided test with a lower critical boundary (side="less"
) or a one-sided test with an upper critical boundary (side="greater"
).- scale
Optional. Scaling function for global envelopes. A function in the R language which determines the relative scale of deviations, as a function of distance \(r\), when computing the global envelopes. Applicable only when
global=TRUE
. Summary function values for distancer
will be divided byscale(r)
before the maximum deviation is computed. The resulting global envelopes will have width proportional toscale(r)
.- clamp
Logical value indicating how to compute envelopes when
alternative="less"
oralternative="greater"
. Deviations of the observed summary function from the theoretical summary function are initially evaluated as signed real numbers, with large positive values indicating consistency with the alternative hypothesis. Ifclamp=FALSE
(the default), these values are not changed. Ifclamp=TRUE
, any negative values are replaced by zero.- savefuns
Logical flag indicating whether to save all the simulated function values.
- savepatterns
Logical flag indicating whether to save all the simulated point patterns.
- nsim2
Number of extra simulated point patterns to be generated if it is necessary to use simulation to estimate the theoretical mean of the summary function. Only relevant when
global=TRUE
and the simulations are not based on CSR.- VARIANCE
Logical. If
TRUE
, critical envelopes will be calculated as sample mean plus or minusnSD
times sample standard deviation.- nSD
Number of estimated standard deviations used to determine the critical envelopes, if
VARIANCE=TRUE
.- Yname
Character string that should be used as the name of the data point pattern
Y
when printing or plotting the results.- maxnerr
Maximum number of rejected patterns. If
fun
yields a fatal error when applied to a simulated point pattern (for example, because the pattern is empty andfun
requires at least one point), the pattern will be rejected and a new random point pattern will be generated. If this happens more thanmaxnerr
times, the algorithm will give up.- rejectNA
Logical value specifying whether to reject a simulated pattern if the resulting values of
fun
are all equal toNA
,NaN
or infinite. IfFALSE
(the default), then simulated patterns are only rejected whenfun
gives a fatal error.- silent
Logical value specifying whether to print a report each time a simulated pattern is rejected.
- do.pwrong
Logical. If
TRUE
, the algorithm will also estimate the true significance level of the “wrong” test (the test that declares the summary function for the data to be significant if it lies outside the pointwise critical boundary at any point). This estimate is printed when the result is printed.- envir.simul
Environment in which to evaluate the expression
simulate
, if not the current environment.
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 generatensim
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 patternY
.If
simulate
is supplied, then it determines how the simulated point patterns are generated. Seeenvelope
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
.
Value
A function value table (object of class "fv"
)
which can be plotted directly.
See envelope
for further details.
References
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.
See Also
Examples
# NOT RUN {
X <- rpoispp3(20, box3())
# }
# NOT RUN {
plot(envelope(X, nsim=39))
# }
# NOT RUN {
# }