spatstat (version 1.23-1)

envelope.pp3: Simulation Envelopes of Summary Function for 3D Point Pattern

Description

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

Usage

## S3 method for class 'pp3':
envelope(Y, fun=K3est, nsim=99, nrank=1, \dots, 
  simulate=NULL, verbose=TRUE, 
  transform=NULL,global=FALSE,ginterval=NULL,
  savefuns=FALSE, savepatterns=FALSE,
  nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL, maxnerr=nsim)

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.

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

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.

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 an 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 a

Value

• A function value table (object of class "fv") which can be plotted directly. See envelope for further details.

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.

• Ifsimulate=NULL, then we generatensimsimulations of Complete Spatial Randomness (i.e.nsimsimulated point patterns each being a realisation of the uniform Poisson point process) with the same intensity as the patternY.
• Ifsimulateis supplied, then it determines how the simulated point patterns are generated. Seeenvelopefor 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.

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

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

Examples

X <- rpoispp3(20, box3())
 plot(envelope(X, nsim=39))
 <testonly>plot(envelope(X, nsim=4))</testonly>