spatstat (version 1.23-1)

envelope.lpp: Envelope for Point Patterns on Linear Network

Description

Enables envelopes to be computed for point patterns on a linear network.

Usage

## S3 method for class 'lpp':
envelope(Y, fun=linearK, 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)
  ## S3 method for class 'lppm':
envelope(Y, fun=linearK, 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)

Arguments

Y

A point pattern on a linear network (object of class "lpp") or a fitted point process model on a linear network (object of class "lppm").

fun

Function that is to be computed for each simulated pattern.

nsim

Number of simulations to perform.

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.

Value

• Function value table (object of class "fv") with additional information, as described in envelope.

Details

This is a method for the generic function envelope applicable to point patterns on a linear network. The argument Y can be either a point pattern on a linear network, or a fitted point process model on a linear network. The function fun will be evaluated for the data and also for nsim simulated point patterns on the same linear network. The upper and lower envelopes of these evaluated functions will be computed as described in envelope. The type of simulation is determined as follows.

• ifYis a point pattern (object of class"lpp") andsimulateis missing orNULL, then random point patterns will be generated according to a Poisson point process on the linear network on whichYis defined, with intensity estimated fromY.
• ifYis a fitted point process model (object of class"lppm") andsimulateis missing orNULL, then random point patterns will be generated by simulating from the fitted model.
• Ifsimulateis present, it should be an expression that can be evaluated to yield random point patterns on the same linear network asY.

The function fun should accept as its first argument a point pattern on a linear network (object of class "lpp") and should have another argument called r or a ... argument.

References

Ang, Q.W. (2010) Statistical methodology for events on a network. Master's thesis, School of Mathematics and Statistics, University of Western Australia. Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. To appear in Scandinavian Journal of Statistics. Okabe, A. and Yamada, I. (2001) The K-function method on a network and its computational implementation. Geographical Analysis 33, 271-290.

See Also

envelope, linearK

Examples

example(lpp)
   # uniform Poisson
   envelope(X, nsim=4)
   # nonuniform Poisson
   fit <- lppm(X, ~x)
   envelope(fit, nsim=4)