# 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(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 \(h_{ij}\) 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))`

.

##### 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.

##### See Also

`ppm`

,
`pairwise.family`

,
`ppm.object`

,
`MultiStrauss`

,
`MultiHard`

,
`Strauss`

##### Examples

```
# NOT RUN {
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
# }
# NOT RUN {
fit <- ppm(X ~1, MultiStraussHard(r,h))
# fit stationary multitype hardcore Strauss process to `amacrine'
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*