R: The Multitype/Hard Core Strauss Point Process Model

MultiStraussHard {spatstat.core} | R Documentation

## The Multitype/Hard Core Strauss Point Process Model

### Description

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

### Usage

      MultiStraussHard(iradii, hradii, types=NULL)

### Arguments

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

### Details

This is a hybrid of the multitype Strauss process (see `MultiStrauss`) and the hard core process (case gamma = 0 of the Strauss process). A pair of points of types i and j must not lie closer than h[i,j] units apart; if the pair lies more than h[i,j] and less than r[i,j] units apart, it contributes a factor gamma[i,j] to the probability density.

The argument `types` need not be specified in normal use. It will be determined automatically from the point pattern data set to which the MultiStraussHard 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 matrices `iradii` and `hradii`.

The matrices `iradii` and `hradii` 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 and hardcore radii are specified in `MultiStraussHard`. The canonical parameters log(beta[j]) and log(gamma[i,j]) are estimated by `ppm()`, not fixed in `MultiStraussHard()`.

### Value

An object of class `"interact"` describing the interpoint interaction structure of the multitype/hard core Strauss process with interaction radii iradii[i,j] and hard core radii hradii[i,j].

### Warnings

In order that `ppm` can fit the multitype/hard core 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: `MultiStraussHard(types=NULL, iradii, hradii)`. 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`, `MultiStrauss`, `MultiHard`, `Strauss`

### Examples

       r <- matrix(3, nrow=2,ncol=2)
       h <- matrix(c(1,2,2,1), nrow=2,ncol=2)
       MultiStraussHard(r,h)
       # prints a sensible description of itself
       r <- 0.04 * matrix(c(1,2,2,1), nrow=2,ncol=2)
       h <- 0.02 * matrix(c(1,NA,NA,1), nrow=2,ncol=2)
       X <- amacrine

       fit <- ppm(X ~1, MultiStraussHard(r,h))
       # fit stationary multitype hardcore Strauss process to `amacrine'

[Package spatstat.core version 2.3-1 Index]