# MultiHard

##### The Multitype Hard Core Point Process Model

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

##### Usage

`MultiHard(hradii, types=NULL)`

##### Arguments

- 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 multitype version of the hard core process. A pair of points of types \(i\) and \(j\) must not lie closer than \(h_{ij}\) units apart.

The argument `types`

need not be specified in normal use.
It will be determined automatically from the point pattern data set
to which the MultiStrauss 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 matrix `hradii`

.

The matrix `hradii`

must be symmetric, with entries
which are either positive numbers or `NA`

.
A value of `NA`

indicates that no distance constraint should be applied
for this combination of types.

Note that only the hardcore radii
are specified in `MultiHard`

.
The canonical parameters \(\log(\beta_j)\)
are estimated by `ppm()`

, not fixed in
`MultiHard()`

.

##### Value

An object of class `"interact"`

describing the interpoint interaction
structure of the multitype hard core process with
hard core radii \(hradii[i,j]\).

##### Warnings

In order that `ppm`

can fit the multitype hard core
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:
`MultiHard(types=NULL, hradii)`

.
The new code attempts to handle the old syntax as well.

##### See Also

`ppm`

,
`pairwise.family`

,
`ppm.object`

,
`MultiStrauss`

,
`MultiStraussHard`

,
`Strauss`

.

See `ragsMultiHard`

and `rmh`

for
simulation.

##### Examples

```
# NOT RUN {
h <- matrix(c(1,2,2,1), nrow=2,ncol=2)
# prints a sensible description of itself
MultiHard(h)
# Fit the stationary multitype hardcore process to `amacrine'
# with hard core operating only between cells of the same type.
h <- 0.02 * matrix(c(1, NA, NA, 1), nrow=2,ncol=2)
ppm(amacrine ~1, MultiHard(h))
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*