# 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(types=NULL, hradii)`

##### Arguments

- types
- Optional; vector of all possible types (i.e. the possible levels
of the
`marks`

variable in the data) - hradii
- Matrix of hard core radii

##### 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))`

.

##### See Also

`ppm`

,
`pairwise.family`

,
`ppm.object`

,
`MultiStrauss`

,
`MultiStraussHard`

,
`Strauss`

##### Examples

```
h <- matrix(c(1,2,2,1), nrow=2,ncol=2)
MultiHard(hradii=h)
# prints a sensible description of itself
data(betacells)
h <- 15.0 * matrix(c(NA,1,1,NA), nrow=2,ncol=2)
ppm(betacells, ~1, MultiHard(,h))
# fit the stationary multitype hardcore process to `betacells'
# Note the comma; needed since "types" is not specified.
```

*Documentation reproduced from package spatstat, version 1.23-5, License: GPL (>= 2)*