R: Compute or Extract Effective Range of Cluster Kernel

clusterradius {spatstat.core} | R Documentation

## Compute or Extract Effective Range of Cluster Kernel

### Description

Given a cluster point process model, this command returns a value beyond which the the probability density of the cluster offspring is neglible.

### Usage

    clusterradius(model, ...)

    ## S3 method for class 'kppm'
    clusterradius(model, ..., thresh = NULL, precision = FALSE)

    ## S3 method for class 'character'
    clusterradius(model, ..., thresh = NULL, precision = FALSE)

### Arguments

`model` | Cluster model. Either a fitted cluster or Cox model (object of class `"kppm"`), or a character string specifying the type of cluster model.
`...` | Parameter values for the model, when `model` is a character string.
`thresh` | Numerical threshold relative to the cluster kernel value at the origin (parent location) determining when the cluster kernel will be considered neglible. A sensible default is provided.
`precision` | Logical. If `precision=TRUE` the precision of the calculated range is returned as an attribute to the range. See details.

### Details

Given a cluster model this function by default returns the effective range of the model with the given parameters as used in spatstat. For the Matern cluster model (see e.g. `rMatClust`) this is simply the finite radius of the offsring density given by the paramter `scale` irrespective of other options given to this function. The remaining models in spatstat have infinite theoretical range, and an effective finite value is given as follows: For the Thomas model (see e.g. `rThomas` the default is `4*scale` where scale is the scale or standard deviation parameter of the model. If `thresh` is given the value is instead found as described for the other models below.

For the Cauchy model (see e.g. `rCauchy`) and the Variance Gamma (Bessel) model (see e.g. `rVarGamma`) the value of `thresh` defaults to 0.001, and then this is used to compute the range numerically as follows. If k(x,y)=k0(r) with r=sqrt(x^2+y^2) denotes the isotropic cluster kernel then f(r) = 2 π r k0(r) is the density function of the offspring distance from the parent. The range is determined as the value of r where f(r) falls below `thresh` times k0(r).

If `precision=TRUE` the precision related to the chosen range is returned as an attribute. Here the precision is defined as the polar integral of the kernel from distance 0 to the calculated range. Ideally this should be close to the value 1 which would be obtained for the true theretical infinite range.

### Value

A positive numeric.

Additionally, the precision related to this range value is returned as an attribute `"prec"`, if `precision=TRUE`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### See Also

`clusterkernel`, `kppm`, `rMatClust`, `rThomas`, `rCauchy`, `rVarGamma`, `rNeymanScott`.

### Examples

      fit <- kppm(redwood ~ x, "MatClust")
      clusterradius(fit)

      clusterradius("Thomas", scale = .1)
      clusterradius("Thomas", scale = .1, thresh = 0.001)
      clusterradius("VarGamma", scale = .1, nu = 2, precision = TRUE)

[Package spatstat.core version 2.3-1 Index]