R: Interaction Distance of a Point Process

reach {spatstat.core} | R Documentation

## Interaction Distance of a Point Process

### Description

Computes the interaction distance of a point process.

### Usage

      reach(x, ...)

      ## S3 method for class 'ppm'
    reach(x, ..., epsilon=0)

      ## S3 method for class 'interact'
    reach(x, ...)

      ## S3 method for class 'rmhmodel'
    reach(x, ...)

      ## S3 method for class 'fii'
    reach(x, ..., epsilon)

### Arguments

`x` | Either a fitted point process model (object of class `"ppm"`), an interpoint interaction (object of class `"interact"`), a fitted interpoint interaction (object of class `"fii"`) or a point process model for simulation (object of class `"rmhmodel"`).
`epsilon` | Numerical threshold below which interaction is treated as zero. See details.
`...` | Other arguments are ignored.

### Details

The ‘interaction distance’ or ‘interaction range’ of a point process model of class `"ppm"` is the smallest distance D such that any two points in the process which are separated by a distance greater than D do not interact with each other.

For example, the interaction range of a Strauss process (see `Strauss`) with parameters beta,gamma,r is equal to r, unless gamma=1 in which case the model is Poisson and the interaction range is 0. The interaction range of a Poisson process is zero. The interaction range of the Ord threshold process (see `OrdThresh`) is infinite, since two points may interact at any distance apart.

The function `reach(x)` is generic, with methods for the case where `x` is

- a fitted point process model (object of class `"ppm"`, usually obtained from the model-fitting function `ppm`);

- an interpoint interaction structure (object of class `"interact"`), created by one of the functions `Poisson`, `Strauss`, `StraussHard`, `MultiStrauss`, `MultiStraussHard`, `Softcore`, `DiggleGratton`, `Pairwise`, `PairPiece`, `Geyer`, `LennardJones`, `Saturated`, `OrdThresh` or `Ord`;

- a fitted interpoint interaction (object of class `"fii"`) extracted from a fitted point process model by the command `fitin`;

- a point process model for simulation (object of class `"rmhmodel"`), usually obtained from `rmhmodel`.

When `x` is an `"interact"` object, `reach(x)` returns the maximum possible interaction range for any point process model with interaction structure given by `x`. For example, `reach(Strauss(0.2))` returns `0.2`.

When `x` is a `"ppm"` object, `reach(x)` returns the interaction range for the point process model represented by `x`. For example, a fitted Strauss process model with parameters `beta,gamma,r` will return either `0` or `r`, depending on whether the fitted interaction parameter `gamma` is equal or not equal to 1.

For some point process models, such as the soft core process (see `Softcore`), the interaction distance is infinite, because the interaction terms are positive for all pairs of points. A practical solution is to compute the distance at which the interaction contribution from a pair of points falls below a threshold `epsilon`, on the scale of the log conditional intensity. This is done by setting the argument `epsilon` to a positive value.

### Value

The interaction distance, or `NA` if this cannot be computed from the information given.

### Other types of models

Methods for `reach` are also defined for point process models of class `"kppm"` and `"dppm"`. Their technical definition is different from this one. See `reach.kppm` and `reach.dppm`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

### See Also

`ppm`, `Poisson`, `Strauss`, `StraussHard`, `MultiStrauss`, `MultiStraussHard`, `Softcore`, `DiggleGratton`, `Pairwise`, `PairPiece`, `Geyer`, `LennardJones`, `Saturated`, `OrdThresh`, `Ord`, `rmhmodel`

See `reach.kppm` and `reach.dppm` for other types of point process models.

### Examples

        reach(Poisson())
        # returns 0

        reach(Strauss(r=7))
        # returns 7
        fit <- ppm(swedishpines ~ 1, Strauss(r=7))
        reach(fit)
        # returns 7

        reach(OrdThresh(42))
        # returns Inf

        reach(MultiStrauss(matrix(c(1,3,3,1),2,2)))
        # returns 3

[Package spatstat.core version 1.65-5 Index]