spatstat (version 1.48-0)

default.expand: Default Expansion Rule for Simulation of Model

Description

Defines the default expansion window or expansion rule for simulation of a fitted point process model.

Usage

default.expand(object, m=2, epsilon=1e-6, w=Window(object))

Arguments

object

A point process model (object of class "ppm" or "rmhmodel").

m

A single numeric value. The window will be expanded by a distance m * reach(object) along each side.

epsilon

Threshold argument passed to reach to determine reach(object).

w

Optional. The un-expanded window in which the model is defined. The resulting simulated point patterns will lie in this window.

Value

A window expansion rule (object of class "rmhexpand").

Details

This function computes a default value for the expansion rule (the argument expand in rmhcontrol) given a fitted point process model object. This default is used by envelope, qqplot.ppm, simulate.ppm and other functions.

Suppose we wish to generate simulated realisations of a fitted point process model inside a window w. It is advisable to first simulate the pattern on a larger window, and then clip it to the original window w. This avoids edge effects in the simulation. It is called expansion of the simulation window. Accordingly, for the Metropolis-Hastings simulation algorithm rmh, the algorithm control parameters specified by rmhcontrol include an argument expand that determines the expansion of the simulation window.

The function default.expand determines the default expansion rule for a fitted point process model object. If the model is Poisson, then no expansion is necessary. No expansion is performed by default, and default.expand returns a rule representing no expansion. The simulation window is the original window w = Window(object). If the model depends on external covariates (i.e.\ covariates other than the Cartesian covariates x and y and the marks) then no expansion is feasible, in general, because the spatial domain of the covariates is not guaranteed to be large enough. default.expand returns a rule representing no expansion. The simulation window is the original window w = Window(object).

If the model depends on the Cartesian covariates x and y, it would be feasible to expand the simulation window, and this was the default for spatstat version 1.24-1 and earlier. However this sometimes produces artefacts (such as an empty point pattern) or memory overflow, because the fitted trend, extrapolated outside the original window of the data, may become very large. In spatstat version 1.24-2 and later, the default rule is not to expand if the model depends on x or y. Again default.expand returns a rule representing no expansion. Otherwise, expansion will occur. The original window w = Window(object) is expanded by a distance m * rr, where rr is the interaction range of the model, computed by reach. If w is a rectangle then each edge of w is displaced outward by distance m * rr. If w is not a rectangle then w is dilated by distance m * rr using dilation.

See Also

rmhexpand, rmhcontrol, rmh, envelope, qqplot.ppm

Examples

  data(cells)
  fit <- ppm(cells, ~1, Strauss(0.07))
  default.expand(fit)
  mod <- rmhmodel(cif="strauss", par=list(beta=100, gamma=0.5, r=0.07))
  default.expand(fit)