R: Penttinen Interaction

Penttinen {spatstat.core} | R Documentation

## Penttinen Interaction

### Description

Creates an instance of the Penttinen pairwise interaction point process model, which can then be fitted to point pattern data.

### Usage

      Penttinen(r)

### Arguments

`r` | circle radius

### Details

Penttinen (1984, Example 2.1, page 18), citing Cormack (1979), described the pairwise interaction point process with interaction factor

h(d) = exp(theta * A(d)) = gamma^(A(d))

between each pair of points separated by a distance $d$. Here A(d) is the area of intersection between two discs of radius r separated by a distance d, normalised so that A(0) = 1.

The scale of interaction is controlled by the disc radius r: two points interact if they are closer than 2 * r apart. The strength of interaction is controlled by the canonical parameter theta, which must be less than or equal to zero, or equivalently by the parameter gamma = exp(theta), which must lie between 0 and 1.

The potential is inhibitory, i.e.\ this model is only appropriate for regular point patterns. For gamma=0 the model is a hard core process with hard core diameter 2 * r. For gamma=1 the model is a Poisson process.

The irregular parameter r must be given in the call to `Penttinen`, while the regular parameter theta will be estimated.

This model can be considered as a pairwise approximation to the area-interaction model `AreaInter`.

### Value

An object of class `"interact"` describing the interpoint interaction structure of a point process.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk

### References

Cormack, R.M. (1979) Spatial aspects of competition between individuals. Pages 151–212 in Spatial and Temporal Analysis in Ecology, eds. R.M. Cormack and J.K. Ord, International Co-operative Publishing House, Fairland, MD, USA.

Penttinen, A. (1984) Modelling Interaction in Spatial Point Patterns: Parameter Estimation by the Maximum Likelihood Method. Jyvaskyla Studies in Computer Science, Economics and Statistics 7, University of Jyvaskyla, Finland.

### See Also

`ppm`, `ppm.object`, `Pairwise`, `AreaInter`.

### Examples

       fit <- ppm(cells ~ 1, Penttinen(0.07))
       fit
       reach(fit) # interaction range is circle DIAMETER

[Package spatstat.core version 2.0-0 Index]