# DiggleGratton

0th

Percentile

##### 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 $$h(t) = \left( \frac{t-\delta}{\rho-\delta} \right)^\beta \quad\quad \mbox{ if } \delta \le t \le \rho$$ 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.

##### Value

• An object of class "interact" describing the interpoint interaction structure of a point process.

##### 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

##### Aliases
• DiggleGratton
##### 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
Documentation reproduced from package spatstat, version 1.1-3, License: GPL version 2 or newer

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