repul: Repulsiveness Index of a Point Process Model

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

Repulsiveness Index of a Point Process Model

Description

Computes a measure of the degree of repulsion between points in a point process model.

Usage

repul(model, ...)

## S3 method for class 'dppm'
repul(model, ...)

## S3 method for class 'detpointprocfamily'
repul(model, ...)

## S3 method for class 'clusterprocess'
repul(model, ...)

## S3 method for class 'kppm'
repul(model, ...)

## S3 method for class 'ppm'
repul(model, ...)

## S3 method for class 'slrm'
repul(model, ...)

## S3 method for class 'rppm'
repul(model, ...)

## S3 method for class 'mppm'
repul(model, ...)

Arguments

model	A fitted point process model (object of class "dppm", "kppm", "ppm", "slrm", "rppm" or "mppm") or a point process specified by its parameters (object of class "detpointprocfamily" or "clusterprocess").
...	Ignored.

Details

The repulsiveness index \mu of a point process model was defined by Lavancier, \Moller and Rubak (2015) as

\mu = \lambda \int (1- g(x)) \, dx

where \lambda is the intensity of the model and g(x) is the pair correlation function, and the integral is taken over all two-dimensional vectors x.

Values of \mu are dimensionless. Larger positive values of \mu indicate stronger repulsion between points.

The repulsiveness index was originally defined for determinantal point processes, but the same definition can be applied to other kinds of point process models. The repulsiveness index is positive for a determinantal point process model, zero for a Poisson process or spatial logistic regression model, negative for a cluster process or Cox process, and typically positive for a Gibbs process.

If the model is stationary, the result is a single number.

If the model is not stationary, the result is a pixel image (obtained by multiplying the spatially-varying intensity by the integral defined above).

For Gibbs models of class "ppm" the calculation uses the Poisson-saddlepoint approximation to the pair correlation function, and is only implemented for stationary unmarked processes.

For models of class "mppm" the result is a numeric vector or a list of images, with one entry for each point pattern to which the model was fitted.

Value

A numeric value or a pixel image.

Author(s)

\adrian

.

References

Lavancier, F., \Moller, J. and Rubak, E. (2015), Determinantal point process models and statistical inference. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77, 853–877.

See Also

dppm, psib.

Examples

  jpines <- residualspaper$Fig1
  
  fit <- dppm(jpines ~ 1, dppGauss)
  repul(fit)

  m <- dppGauss(lambda=10, alpha=0.1, d=2)
  repul(m)

  repul(kppm(redwood ~ 1))

spatstat.model documentation built on July 28, 2026, 9:06 a.m.