spatstat (version 1.64-1)

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

Value

A positive numeric.

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

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 \(k(x,y)=k_0(r)\) with \(r=\sqrt(x^2+y^2)\) denotes the isotropic cluster kernel then \(f(r) = 2 \pi r k_0(r)\) 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 \(k_0(r)\).

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.

See Also

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

Examples

# NOT RUN {
  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)
# }