The Multitype Strauss Point Process Model
Creates an instance of the multitype Strauss point process model which can then be fitted to point pattern data.
MultiStrauss(radii, types=NULL)
radii |
Matrix of interaction radii |
types |
Optional; vector of all possible types (i.e. the possible levels
of the |
The (stationary) multitype Strauss process with m types, with interaction radii r[i,j] and parameters beta[j] and gamma[i,j] 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[i,j] units apart contributes a factor gamma[i,j] 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[i,j]) are estimated by
ppm(), not fixed in MultiStrauss().
An object of class "interact"
describing the interpoint interaction
structure of the multitype Strauss process with
interaction radii radii[i,j].
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)).
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
, Rolf Turner r.turner@auckland.ac.nz
and Ege Rubak rubak@math.aau.dk
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 trendPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.