R: Default Expansion Rule for Simulation of Model

default.expand {spatstat.core} | R Documentation

## 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.

### 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`.

### Value

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

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### 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)

[Package spatstat.core version 2.3-0 Index]