| MultiStrauss {spatstat} | R Documentation |
Creates an instance of the multitype Strauss point process model which can then be fitted to point pattern data.
MultiStrauss(types, radii)
types |
Vector of all possible types (i.e. the possible levels
of the marks variable in the data) |
radii |
Matrix of interaction radii |
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 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
Strauss().
An object of class "interact"
describing the interpoint interaction
structure of the multitype Strauss process with
interaction radii radii[i,j].
The argument types is interpreted as a
set of factor levels. That is,
in order that ppm can fit the multitype Strauss model
correctly to a point pattern X,
this must be a marked point pattern; the mark vector
X$marks must be a factor; and
the argument types must
equal levels(X$marks).
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
ppm,
pairwise.family,
ppm.object,
Strauss
r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
MultiStrauss(1:2, r)
# prints a sensible description of itself
data(betacells)
r <- 30.0 * matrix(c(1,2,2,1), nrow=2,ncol=2)
ppm(betacells, ~1, MultiStrauss(c("off","on"), r), rbord=60.0)
# fit the stationary multitype Strauss process to `betacells'
ppm(betacells, ~polynom(x,y,3), MultiStrauss(c("off","on"), r), rbord=60.0)
# fit a nonstationary Strauss process with log-cubic polynomial trend