# 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

```
DiggleGatesStibbard(0.02)
# prints a sensible description of itself
data(cells)
ppm(cells, ~1, DiggleGatesStibbard(0.05))
# fit the stationary D-G-S process to `cells'
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 1.31-2, License: GPL (>= 2)*