spatstat.local (version 5.1-0)

psib.loccit: Sibling Probability of Locally Fitted Cluster Point Process

Description

Computes the sibling probability of a locally fitted cluster point process model.

Usage

# S3 method for loccit
psib(object)
  # S3 method for locmincon
psib(object)

Value

A spatially sampled function (object of class

"ssf") giving the spatially-varying sibling probability.

Arguments

object

Fitted cluster point process model (object of class "loccit" or "locmincon").

Author

Adrian Baddeley .

Details

In a Poisson cluster process, two points are called siblings if they belong to the same cluster, that is, if they had the same parent point. If two points of the process are separated by a distance \(r\), the probability that they are siblings is \(p(r) = 1 - 1/g(r)\) where \(g\) is the pair correlation function of the process.

The value \(p(0) = 1 - 1/g(0)\) is the probability that, if two points of the process are situated very close to each other, they came from the same cluster. This probability is an index of the strength of clustering, with high values suggesting strong clustering.

This concept was proposed in Baddeley, Rubak and Turner (2015, page 479) and Baddeley (2016).

The function psib is generic, with methods for "kppm", "loccit" and "locmincon".

The functions described here are the methods for locally-fitted cluster models of class "loccit" and "locmincon". They compute the spatially-varying sibling probability of the locally-fitted model.

References

Baddeley, A. (2017) Local composite likelihood

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

See Also

psib, kppm, loccit

Examples

   if (FALSE) {
   fit <- loccit(redwood, ~1, "Thomas")
   }
   # \testonly{
   X <- redwood[owin(c(0,1), c(-1,-1/2))]
   fit <- loccit(X, ~1, "Thomas", nd=5, control=list(maxit=20))
   # }
   fit
   plot(psib(fit))