MultiStraussHard
The Multitype/Hard Core Strauss Point Process Model
Creates an instance of the multitype/hard core Strauss point process model which can then be fitted to point pattern data.
Usage
MultiStraussHard(types=NULL, iradii, hradii)Arguments
- types
- Optional; vector of all possible types (i.e. the possible levels
of the
marksvariable in the data) - iradii
- Matrix of interaction radii
- hradii
- Matrix of hard core radii
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 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 $\log(\gamma_{ij})$
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)).
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(iradii=r,hradii=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)
ppm(amacrine, ~1, MultiStraussHard(,r,h))
# fit stationary multitype hardcore Strauss process to `amacrine'
# Note the comma; needed since "types" is not specified.