| MultiStrauss {spatstat.model} | R Documentation |
The Multitype Strauss Point Process Model
Description
Creates an instance of the multitype Strauss point process model which can then be fitted to point pattern data.
Usage
MultiStrauss(radii, types=NULL)
Arguments
radii |
Matrix of interaction radii |
types |
Optional; vector of all possible types (i.e. the possible levels
of the |
Details
The (stationary) multitype
Strauss process with m types, with interaction radii
r_{ij} and
parameters \beta_j and \gamma_{ij}
is the pairwise interaction 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.
The nonstationary multitype 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 multitype
Strauss process pairwise interaction is
yielded by the function MultiStrauss(). 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 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 radii.
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 MultiStrauss. The canonical
parameters \log(\beta_j) and
\log(\gamma_{ij}) are estimated by
ppm(), not fixed in MultiStrauss().
Value
An object of class "interact"
describing the interpoint interaction
structure of the multitype Strauss process with
interaction radii radii[i,j].
Warnings
In order that ppm can fit the multitype Strauss
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)).
Changed Syntax
Before spatstat version 1.37-0,
the syntax of this function was different:
MultiStrauss(types=NULL, radii).
The new code attempts to handle the old syntax as well.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
See Also
ppm,
pairwise.family,
ppm.object,
Strauss,
MultiHard
Examples
r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
MultiStrauss(r)
# prints a sensible description of itself
r <- 0.03 * matrix(c(1,2,2,1), nrow=2,ncol=2)
X <- amacrine
ppm(X ~1, MultiStrauss(r))
# fit the stationary multitype Strauss process to `amacrine'
ppm(X ~polynom(x,y,3), MultiStrauss(r, c("off","on")))
# fit a nonstationary multitype Strauss process with log-cubic trend