Revision c9b2c621c3bff55aaa77646dc1ba7316765cd7e4 authored by Adrian Baddeley on 25 April 2013, 00:00:00 UTC, committed by Gabor Csardi on 25 April 2013, 00:00:00 UTC
1 parent f86606a
MultiStrauss.Rd
\name{MultiStrauss}
\alias{MultiStrauss}
\title{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(types=NULL, radii)
}
\arguments{
\item{types}{Optional; vector of all possible types (i.e. the possible levels
of the \code{marks} variable in the data)}
\item{radii}{Matrix of interaction radii}
}
\value{
An object of class \code{"interact"}
describing the interpoint interaction
structure of the multitype Strauss process with
interaction radii \eqn{radii[i,j]}.
}
\details{
The (stationary) multitype
Strauss process with \eqn{m} types, with interaction radii
\eqn{r_{ij}}{r[i,j]} and
parameters \eqn{\beta_j}{beta[j]} and \eqn{\gamma_{ij}}{gamma[i,j]}
is the pairwise interaction point process
in which each point of type \eqn{j}
contributes a factor \eqn{\beta_j}{beta[j]} to the
probability density of the point pattern, and a pair of points
of types \eqn{i} and \eqn{j} closer than \eqn{r_{ij}}{r[i,j]}
units apart contributes a factor
\eqn{\gamma_{ij}}{gamma[i,j]} to the density.
The nonstationary multitype Strauss process is similar except that
the contribution of each individual point \eqn{x_i}{x[i]}
is a function \eqn{\beta(x_i)}{beta(x[i])}
of location and type, rather than a constant beta.
The function \code{\link{ppm}()}, which fits point process models to
point pattern data, requires an argument
of class \code{"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 \code{MultiStrauss()}. See the examples below.
The argument \code{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 \code{\link{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 \code{radii}.
The matrix \code{radii} must be symmetric, with entries
which are either positive numbers or \code{NA}.
A value of \code{NA} indicates that no interaction term should be included
for this combination of types.
Note that only the interaction radii are
specified in \code{MultiStrauss}. The canonical
parameters \eqn{\log(\beta_j)}{log(beta[j])} and
\eqn{\log(\gamma_{ij})}{log(gamma[i,j])} are estimated by
\code{\link{ppm}()}, not fixed in \code{MultiStrauss()}.
}
\seealso{
\code{\link{ppm}},
\code{\link{pairwise.family}},
\code{\link{ppm.object}},
\code{\link{Strauss}},
\code{\link{MultiHard}}
}
\examples{
r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
MultiStrauss(radii=r)
# prints a sensible description of itself
r <- 0.03 * matrix(c(1,2,2,1), nrow=2,ncol=2)
X <- amacrine
\testonly{
X <- X[ owin(c(0, 0.8), c(0, 1)) ]
}
ppm(X, ~1, MultiStrauss(, r))
# fit the stationary multitype Strauss process to `amacrine'
# Note the comma; needed since "types" is not specified.
\dontrun{
ppm(X, ~polynom(x,y,3), MultiStrauss(c("off","on"), r))
# fit a nonstationary multitype Strauss process with log-cubic trend
}
}
\section{Warnings}{
In order that \code{\link{ppm}} can fit the multitype Strauss
model correctly to a point pattern \code{X}, this pattern must
be marked, with \code{markformat} equal to \code{vector} and the
mark vector \code{marks(X)} must be a factor. If the argument
\code{types} is specified it is interpreted as a set of factor
levels and this set must equal \code{levels(marks(X))}.
}
\author{Adrian Baddeley
\email{Adrian.Baddeley@csiro.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{models}
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