R: The Multitype Strauss Point Process Model

MultiStrauss {spatstat} | R Documentation

## The Multitype Strauss Point Process Model

### Description

Creates an instance of the multitype Strauss point process model which can then be fitted to point pattern data.

### Usage

      MultiStrauss(radii, types=NULL)

### Arguments

`radii` | Matrix of interaction radii
`types` | Optional; vector of all possible types (i.e. the possible levels of the `marks` variable in the data)

### Details

The (stationary) multitype Strauss process with m types, with interaction radii r[i,j] and parameters beta[j] and gamma[i,j] is the pairwise interaction point process in which each point of type j contributes a factor beta[j] to the probability density of the point pattern, and a pair of points of types i and j closer than r[i,j] units apart contributes a factor gamma[i,j] to the density.

The nonstationary multitype Strauss process is similar except that the contribution of each individual point x[i] is a function beta(x[i]) of location and type, rather than a constant beta.

The function `ppm()`, which fits point process models to point pattern data, requires an argument of class `"interact"` describing the interpoint interaction structure of the model to be fitted. The appropriate description of the multitype Strauss process pairwise interaction is yielded by the function `MultiStrauss()`. See the examples below.

The argument `types` need not be specified in normal use. It will be determined automatically from the point pattern data set to which the MultiStrauss interaction is applied, when the user calls `ppm`. However, the user should be confident that the ordering of types in the dataset corresponds to the ordering of rows and columns in the matrix `radii`.

The matrix `radii` must be symmetric, with entries which are either positive numbers or `NA`. A value of `NA` indicates that no interaction term should be included for this combination of types.

Note that only the interaction radii are specified in `MultiStrauss`. The canonical parameters log(beta[j]) and log(gamma[i,j]) are estimated by `ppm()`, not fixed in `MultiStrauss()`.

### Value

An object of class `"interact"` describing the interpoint interaction structure of the multitype Strauss process with interaction radii radii[i,j].

### Warnings

In order that `ppm` can fit the multitype Strauss model correctly to a point pattern `X`, this pattern must be marked, with `markformat` equal to `vector` and the mark vector `marks(X)` must be a factor. If the argument `types` is specified it is interpreted as a set of factor levels and this set must equal `levels(marks(X))`.

### Changed Syntax

Before spatstat version `1.37-0`, the syntax of this function was different: `MultiStrauss(types=NULL, radii)`. The new code attempts to handle the old syntax as well.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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

and Ege Rubak rubak@math.aau.dk

### See Also

`ppm`, `pairwise.family`, `ppm.object`, `Strauss`, `MultiHard`

### Examples

       r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
       MultiStrauss(r)
       # prints a sensible description of itself
       r <- 0.03 * matrix(c(1,2,2,1), nrow=2,ncol=2)
       X <- amacrine

       ppm(X ~1, MultiStrauss(r))
       # fit the stationary multitype Strauss process to `amacrine'

       ## Not run:
       ppm(X ~polynom(x,y,3), MultiStrauss(r, c("off","on")))
       # fit a nonstationary multitype Strauss process with log-cubic trend

    ## End(Not run)

[Package spatstat version 1.63-3 Index]