R: The Strauss Point Process Model

Strauss {spatstat} | R Documentation

## The Strauss Point Process Model

### Description

Creates an instance of the Strauss point process model which can then be fitted to point pattern data.

### Usage

      Strauss(r)

### Arguments

`r` | The interaction radius of the Strauss process

### Details

The (stationary) Strauss process with interaction radius r and parameters beta and gamma is the pairwise interaction point process in which each point contributes a factor beta to the probability density of the point pattern, and each pair of points closer than r units apart contributes a factor gamma to the density.

Thus the probability density is

f(x_1,…,x_n) = alpha . beta^n(x) gamma^s(x)

where x[1],…,x[n] represent the points of the pattern, n(x) is the number of points in the pattern, s(x) is the number of distinct unordered pairs of points that are closer than r units apart, and alpha is the normalising constant.

The interaction parameter gamma must be less than or equal to 1 so that this model describes an “ordered” or “inhibitive” pattern.

The nonstationary Strauss process is similar except that the contribution of each individual point x[i] is a function beta(x[i]) of location, rather than a constant beta.

The function `ppm()`, which fits point process models to point pattern data, requires an argument of class `"interact"` describing the interpoint interaction structure of the model to be fitted. The appropriate description of the Strauss process pairwise interaction is yielded by the function `Strauss()`. See the examples below.

Note the only argument is the interaction radius `r`. When `r` is fixed, the model becomes an exponential family. The canonical parameters log(beta) and log(gamma) are estimated by `ppm()`, not fixed in `Strauss()`.

### Value

An object of class `"interact"` describing the interpoint interaction structure of the Strauss process with interaction radius r.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

Kelly, F.P. and Ripley, B.D. (1976) On Strauss's model for clustering. Biometrika 63, 357–360.

Strauss, D.J. (1975) A model for clustering. Biometrika 62, 467–475.

### See Also

`ppm`, `pairwise.family`, `ppm.object`

### Examples

       Strauss(r=0.1)
       # prints a sensible description of itself
       data(cells)

       ## Not run:
       ppm(cells, ~1, Strauss(r=0.07))
       # fit the stationary Strauss process to `cells'

    ## End(Not run)

       ppm(cells, ~polynom(x,y,3), Strauss(r=0.07))
       # fit a nonstationary Strauss process with log-cubic polynomial trend

[Package spatstat version 1.54-0 Index]