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
$1,2,...,j1$.
The hierarchical version of the (stationary)
Strauss process with $m$ types, with interaction radii
$r[i,j]$ and
parameters $beta[j]$ and $gamma[i,j]$
is a point process
in which each point of type $j$
contributes a factor $beta[j]$ to the
probability density of the point pattern, and a pair of points
of types $i$ and $j$ closer than $r[i,j]$
units apart contributes a factor
$gamma[i,j]$ to the density
provided $i <= j$.="" the="" nonstationary="" hierarchical="" strauss="" process="" is="" similar="" except="" that="" contribution="" of="" each="" individual="" point="" $x[i]$="" a="" function="" $beta(x[i])$="" location="" and="" type,="" rather="" than="" constant="" beta.="" 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
$1,2, ..., m$ meaning that type $j$
depends on types $1,2, ..., j1$.
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
$log(gamma[i,j])$ 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, 12321240.
Hogmander, H. and Sarkka, A. (1999) Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 10511058.
See Also
MultiStrauss
for the corresponding
symmetrical interaction.
Examples
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