spatstat (version 1.3-4)

DiggleGratton: Diggle-Gratton model

Description

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 B 46, 193 -- 212.

See Also

mpl, ppm.object, Pairwise

Examples

data(cells)
   mpl(cells, ~1, DiggleGratton(0.05, 0.1))
   # NOTE: resulting estimate of beta is 8.569, not exp(8.569) = 5267.54