Compute or Extract Effective Range of Cluster Kernel
Given a cluster point process model, this command returns a value beyond which the the probability density of the cluster offspring is neglible.
## S3 method for class 'kppm': clusterradius(model, \dots, thresh = NULL, precision = FALSE)
## S3 method for class 'character': clusterradius(model, \dots, thresh = NULL, precision = FALSE)
- 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,
modelis a character string.
- 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.
- Logical. If
precision=TRUEthe precision of the calculated range is returned as an attribute to the range. See 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
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 $k_0(r)$.
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.
- A positive numeric.
Additionally, the precision related to this range value is returned as an attribute
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)