clusterstrength: Cluster Strength Index

In spatstat.model: Parametric Statistical Modelling and Inference for the 'spatstat' Family

Cluster Strength Index

Description

Calculate the cluster strength index \varphi for a cluster point process or Cox point process model.

Usage

clusterstrength(object)

Arguments

object

Clustered point process model. Either an object of class "kppm" representing a cluster point process or Cox point process model fitted to point pattern data, or an object of class "clusterprocess" representing a cluster process model with specified parameters.

Details

The cluster strength index of a cluster process model is a numerical index which expresses the strength of clustering. It is defined as (Baddeley et al., 2022, section 10.2)

\varphi = g(0)-1

where g is the pair correlation function of the cluster process.

The index \varphi is dimensionless and takes non-negative values. Values close to zero indicate that the process is close to a Poisson process.

For a cluster process, \varphi is related to the sibling probability p by p = \varphi/(1+\varphi).

For a Cox process with driving random intensity \Lambda(x),

\varphi = \frac{\mbox{var}(\Lambda(0))}{E[\Lambda(0)]^2}

is a measure of the variability of the random intensity.

Value

A single numerical value greater than or equal to zero.

Author(s)

\adrian

.

References

Baddeley, A., Davies, T.M., Hazelton, M.L., Rakshit, S. and Turner, R. (2022) Fundamental problems in fitting spatial cluster process models. Spatial Statistics 52, 100709. DOI: 10.1016/j.spasta.2022.100709

See Also

psib, panysib, persist, repul

Examples

  #' Fit a model to the clustered region of full redwood data
  X <- redwoodfull[redwoodfull.extra$regionII]
  fit <- kppm(X)
  clusterstrength(fit)

  #' Create a Thomas model
  m <- clusterprocess("Thomas", kappa=10, mu=5, scale=0.1)
  clusterstrength(m)

spatstat.model documentation built on March 29, 2026, 9:07 a.m.