# HierHard

##### The Hierarchical Hard Core Point Process Model

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

##### Usage

`HierHard(hradii=NULL, types=NULL, archy=NULL)`

##### Arguments

- hradii
- Optional matrix of hard core distances
- types
- Optional; vector of all possible types (i.e. the possible levels
of the
`marks`

variable in the data) - archy
- Optional: the hierarchical order. See Details.

##### Details

This is a hierarchical point process model
for a multitype point pattern
(`ppm()`

,
which fits point process models to
point pattern data, requires an argument
of class `"interact"`

describing the interpoint interaction
structure of the model to be fitted.
The appropriate description of the hierarchical
hard core process pairwise interaction is
yielded by the function `HierHard()`

. See the examples below.

The argument `types`

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

.

The argument `archy`

can be used to specify a hierarchical
ordering of the types. It can be either a vector of integers
or a character vector matching the possible types.
The default is the sequence
$1,2, \ldots, m$ meaning that type $j$
depends on types $1,2, \ldots, j-1$.
The matrix `iradii`

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

.
A value of zero or `NA`

indicates that no hard core interaction term
should be included for this combination of types.
Note that only the hard core distances are
specified in `HierHard`

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

, not fixed in `HierHard()`

.

##### Value

- An object of class
`"interact"`

describing the interpoint interaction structure of the hierarchical hard core process with hard core distances $hradii[i,j]$.

##### References

Grabarnik, P. and *Ecological Modelling* **220**, 1232--1240.

*Biometrics* **55**, 1051--1058.

##### See Also

`MultiHard`

for the corresponding
symmetrical interaction.

##### Examples

```
h <- matrix(c(4, NA, 10, 15), 2, 2)
HierHard(h)
# prints a sensible description of itself
ppm(ants ~1, HierHard(h))
# fit the stationary hierarchical hard core process to ants data
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*