DiggleGratton {spatstat}R Documentation

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

Details

Diggle and Gratton (1984, pages 208-210) introduced the pairwise interaction point process with pair potential h(t) of the form

h(t) = ((t - delta)/(rho - delta))^beta, { } delta <= t <= rho

with h(t) = 0 for t < delta and h(t) = 1 for t > rho.

Here delta <= 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.

Author(s)

Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf

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

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