spatstat (version 1.23-1)

DiggleGatesStibbard: Diggle-Gates-Stibbard Point Process Model

Description

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

Value

• An object of class "interact" describing the interpoint interaction structure of the Diggle-Gates-Stibbard process with interaction range rho.

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.

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

ppm, pairwise.family, DiggleGratton, ppm.object

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