DiggleGratton
Diggle-Gratton model
Creates an instance of the Diggle-Gratton pairwise interaction point process model, which can then be fitted to point pattern data.
- Keywords
- spatial
Usage
DiggleGratton(delta, rho)Arguments
- delta
- lower threshold $\delta$
- rho
- upper threshold $\rho$
Details
Diggle and Gratton (1984, pages 208-210) introduced the pairwise interaction point process with pair potential $h(t)$ of the form $$h(t) = \left( \frac{t-\delta}{\rho-\delta} \right)^\kappa \quad\quad \mbox{ if } \delta \le t \le \rho$$ with $h(t) = 0$ for $t < \delta$ and $h(t) = 1$ for $t > \rho$. Here $\delta$, $\rho$ and $\kappa$ are parameters.
Note that we use the symbol $\kappa$
where Diggle and Gratton (1984) and Diggle, Gates and Stibbard (1987)
use $\beta$, since in spatstat we reserve the symbol
$\beta$ for an intensity parameter.
The parameters must all be nonnegative, and must satisfy $\delta \le \rho$.
The potential is inhibitory, i.e. this model is only appropriate for regular point patterns. The strength of inhibition increases with $\kappa$. For $\kappa=0$ the model is a hard core process with hard core radius $\delta$. For $\kappa=\infty$ the model is a hard core process with hard core radius $\rho$.
The irregular parameters
$\delta, \rho$ must be given in the call to
DiggleGratton, while the
regular parameter $\kappa$ will be estimated.
Value
- An object of class
"interact"describing the interpoint interaction structure of a point process.
References
Diggle, P.J., Gates, D.J. and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 -- 770.
Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, series B 46, 193 -- 212.
See Also
Examples
data(cells)
ppm(cells, ~1, DiggleGratton(0.05, 0.1))