Creates an instance of the Diggle-Gratton pairwise interaction
point process model, which can then be fitted to point pattern data.
Usage
DiggleGratton(delta, rho)
Arguments
delta
lower threshold $\delta$
rho
upper threshold $\rho$
Value
An object of class "interact"
describing the interpoint interaction
structure of a point process.
Details
Diggle and Gratton (1984, pages 208-210)
introduced the pairwise interaction point
process with pair potential $h(t)$ of the form
$$h(t) = \left( \frac{t-\delta}{\rho-\delta} \right)^\beta
\quad\quad \mbox{ if } \delta \le t \le \rho$$
with $h(t) = 0$ for $t < \delta$
and $h(t) = 1$ for $t > \rho$.
Here $\delta \le \rho$ are irregular parameters.
The potential is inhibitory, i.e. this model is only appropriate for
regular point patterns.
Note that the irregular parameters
$\delta, \rho$ must be fixed, while the
regular parameter $\beta$ will be estimated.
References
Diggle, P.J. and Gratton, R.J. (1984)
Monte Carlo methods of inference for implicit statistical models.
Journal of the Royal Statistical Society, series B46, 193 -- 212.