# default.expand

0th

Percentile

##### Compute Expansion Window for Simulation

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

Keywords
spatial, datagen
##### Usage
default.expand(object, m=2, epsilon=1e-6)
##### Arguments
object
A fitted point process model (object of class "ppp").
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.ppm to determine reach(object).
##### Details

This function computes a default value for the expansion window (the argument expand in rmhcontrol) given a fitted point process model object. This default is used by envelope, qqplot.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 window 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 the value 1, representing no expansion. The simulation window is the original window w = as.owin(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 the value 1, representing no expansion. The simulation window is the original window w = as.owin(object).

Otherwise, the original window w = as.owin(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.

##### Value

• A window (object of class "owin") or the numeric value 1, representing no expansion.

rmhcontrol, rmh, envelope, qqplot.ppm

##### Aliases
• default.expand
##### Examples
data(cells)
fit <- ppm(cells, ~1, Strauss(0.07))
default.expand(fit)
Documentation reproduced from package spatstat, version 1.24-1, License: GPL (>= 2)

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