# DiggleGatesStibbard

##### Diggle-Gates-Stibbard Point Process Model

Creates an instance of the Diggle-Gates-Stibbard point process model which can then be fitted to point pattern data.

##### Usage

`DiggleGatesStibbard(rho)`

##### Arguments

- rho
Interaction range

##### Details

Diggle, Gates and Stibbard (1987) proposed a pairwise interaction point process in which each pair of points separated by a distance \(d\) contributes a factor \(e(d)\) to the probability density, where $$ e(d) = \sin^2\left(\frac{\pi d}{2\rho}\right) $$ for \(d < \rho\), and \(e(d)\) is equal to 1 for \(d \ge \rho\).

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 Diggle-Gates-Stibbard
pairwise interaction is
yielded by the function `DiggleGatesStibbard()`

.
See the examples below.

Note that this model does not have any regular parameters
(as explained in the section on Interaction Parameters
in the help file for `ppm`

).
The parameter \(\rho\) is not estimated by `ppm`

.

##### Value

An object of class `"interact"`

describing the interpoint interaction
structure of the Diggle-Gates-Stibbard
process with interaction range `rho`

.

##### References

Baddeley, A. and Turner, R. (2000)
Practical maximum pseudolikelihood for spatial point patterns.
*Australian and New Zealand Journal of Statistics*
**42**, 283--322.

Ripley, B.D. (1981)
*Spatial statistics*.
John Wiley and Sons.

Diggle, P.J., Gates, D.J., and Stibbard, A. (1987)
A nonparametric estimator for pairwise-interaction point processes.
Biometrika **74**, 763 -- 770.
*Scandinavian Journal of Statistics* **21**, 359--373.

##### See Also

##### Examples

```
# NOT RUN {
DiggleGatesStibbard(0.02)
# prints a sensible description of itself
# }
# NOT RUN {
ppm(cells ~1, DiggleGatesStibbard(0.05))
# fit the stationary D-G-S process to `cells'
# }
# NOT RUN {
ppm(cells ~ polynom(x,y,3), DiggleGatesStibbard(0.05))
# fit a nonstationary D-G-S process
# with log-cubic polynomial trend
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*