# 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 (Hogmander and Sarkka, 1999; Grabarnik and Sarkka, 2009). It is appropriate for analysing multitype point pattern data in which the types are ordered so that the points of type \(j\) depend on the points of type \(1,2,\ldots,j-1\).

The hierarchical version of the (stationary) hard core process with \(m\) types, with hard core distances \(h_{ij}\) and parameters \(\beta_j\), is a point process in which each point of type \(j\) contributes a factor \(\beta_j\) to the probability density of the point pattern. If any pair of points of types \(i\) and \(j\) lies closer than \(h_{ij}\) units apart, the configuration of points is impossible (probability density zero).

The nonstationary hierarchical hard core process is similar except that the contribution of each individual point \(x_i\) is a function \(\beta(x_i)\) of location and type, rather than a constant beta.

The function `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 Sarkka, A. (2009)
Modelling the spatial structure of forest stands by
multivariate point processes with hierarchical interactions.
*Ecological Modelling* **220**, 1232--1240.

Hogmander, H. and
Sarkka, A. (1999)
Multitype spatial point patterns with hierarchical interactions.
*Biometrics* **55**, 1051--1058.

##### See Also

`MultiHard`

for the corresponding
symmetrical interaction.

##### Examples

```
# NOT RUN {
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 1.57-1, License: GPL (>= 2)*