# envelope.pp3

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##### Simulation Envelopes of Summary Function for 3D Point Pattern

Computes simulation envelopes of a summary function for a three-dimensional point pattern.

Keywords
hplot, htest, spatial, iteration
##### 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 data Y 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 evaluated nsim times, to obtain nsim point patterns which are taken as the simulated patterns from which the envelopes are computed. If simulate is a function, then this function will be repeatedly applied to the data pattern Y to obtain nsim simulated patterns. If simulate 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. Alternatively simulate may be an object produced by the envelope 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 when global=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 distance r will be divided by scale(r) before the maximum deviation is computed. The resulting global envelopes will have width proportional to scale(r).

clamp

Logical value indicating how to compute envelopes when alternative="less" or alternative="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. If clamp=FALSE (the default), these values are not changed. If clamp=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 minus nSD 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 and fun requires at least one point), the pattern will be rejected and a new random point pattern will be generated. If this happens more than maxnerr 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 to NA, NaN or infinite. If FALSE (the default), then simulated patterns are only rejected when fun 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 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.

##### 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.

pp3, rpoispp3, K3est, G3est, F3est, pcf3est.

• envelope.pp3
##### Examples
# NOT RUN {
X <- rpoispp3(20, box3())

# }
# NOT RUN {
plot(envelope(X, nsim=39))

# }
# NOT RUN {

# }

Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)

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