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, 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
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()
.
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)
.
See Also
Examples
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 <- 15.0 * matrix(c(NA,1,1,NA), nrow=2,ncol=2)
ppm(betacells, ~1, MultiStraussHard(c("off","on"), r, h))
# fit the stationary multitype hardcore Strauss process to `betacells'