StraussHard

The Strauss / Hard Core Point Process Model

Creates an instance of the ``Strauss/ hard core'' point process model which can then be fitted to point pattern data.

Usage

StraussHard(r, hc)

Details

A Strauss/hard core process with interaction radius $r$, hard core distance $h < r$, and parameters $\beta$ and $\gamma$, is a pairwise interaction point process in which

• distinct points are not allowed to come closer than a distance$h$apart
• each pair of points closer than$r$units apart contributes a factor$\gamma$to the probability density.

eqn

$\log(\gamma)$

deqn

$$f(x_1,\ldots,x_n) = \alpha \beta^{n(x)} \gamma^{s(x)}$$

code

StraussHard()

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.

Strauss, D.J. (1975) A model for clustering. Biometrika 63, 467--475.

See Also

mpl, pairwise.family, ppm.object

Aliases

• StraussHard

Examples

library(spatstat)
   StraussHard(r=1,hc=0.02)
   # prints a sensible description of itself

   data(cells) 
   mpl(cells, ~1, StraussHard(r=0.1, hc=0.05), rbord=0.1)
   # fit the stationary Strauss/hard core  process to `cells'

   mpl(cells, ~ polynom(x,y,3), StraussHard(r=0.1, hc=0.05), rbord=0.1)
   # fit a nonstationary Strauss/hard core process
   # with log-cubic polynomial trend