# HierStrauss

##### The Hierarchical Strauss Point Process Model

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

##### Usage

`HierStrauss(radii, types=NULL, archy=NULL)`

##### Arguments

- radii
Matrix of interaction radii

- 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)
Strauss process with \(m\) types, with interaction radii
\(r_{ij}\) and
parameters \(\beta_j\) and \(\gamma_{ij}\)
is a point process
in which each point of type \(j\)
contributes a factor \(\beta_j\) to the
probability density of the point pattern, and a pair of points
of types \(i\) and \(j\) closer than \(r_{ij}\)
units apart contributes a factor
\(\gamma_{ij}\) to the density
**provided** \(i \le j\).

The nonstationary hierarchical Strauss 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
Strauss process pairwise interaction is
yielded by the function `HierStrauss()`

. 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 HierStrauss 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 `radii`

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 are
specified in `HierStrauss`

. The canonical
parameters \(\log(\beta_j)\) and
\(\log(\gamma_{ij})\) are estimated by
`ppm()`

, not fixed in `HierStrauss()`

.

##### Value

An object of class `"interact"`

describing the interpoint interaction
structure of the hierarchical Strauss process with
interaction radii \(radii[i,j]\).

##### 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

`MultiStrauss`

for the corresponding
symmetrical interaction.

##### Examples

```
# NOT RUN {
r <- matrix(10 * c(3,4,4,3), nrow=2,ncol=2)
HierStrauss(r)
# prints a sensible description of itself
ppm(ants ~1, HierStrauss(r, , c("Messor", "Cataglyphis")))
# fit the stationary hierarchical Strauss process to ants data
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*