MultiStraussHard: 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(types, iradii, hradii)

Arguments

types

Vector of all possible types (i.e. the possible levels of the marks variable in the data)

iradii

Matrix of interaction radii

hradii

Matrix of hard core radii

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

The argument types is interpreted as a set of factor levels. That is, in order that ppm can fit the multitype Strauss model correctly to a point pattern X, this must be a marked point pattern; the mark vector X$marks must be a factor; and the argument types must equal levels(X$marks).

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 $h_{ij}$ units apart; if the pair lies more than $h_{ij}$ and less than $r_{ij}$ units apart, it contributes a factor $\gamma_{ij}$ to the probability density.

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 $\log(\gamma_{ij})$ are estimated by ppm(), not fixed in MultiStraussHard().

Examples

Run this code

r <- matrix(3, nrow=2,ncol=2)
   h <- matrix(c(1,2,2,1), nrow=2,ncol=2)
   MultiStraussHard(1:2, r, h)
   # prints a sensible description of itself
   data(betacells)
   r <- 30.0 * matrix(c(1,2,2,1), nrow=2,ncol=2)
   h <- 30.0 * matrix(c(NA,1,1,NA), nrow=2,ncol=2)
   ppm(betacells, ~1, MultiStraussHard(c("off","on"), r, h), rbord=60.0)
   # fit the stationary multitype hardcore Strauss process to `betacells'

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