https://github.com/cran/spatstat
Tip revision: abb5a4feab9cc3cc545376d5688c8359c9bf9194 authored by Adrian Baddeley on 18 December 2008, 07:25:14 UTC
version 1.14-9
version 1.14-9
Tip revision: abb5a4f
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, radii)
}
\arguments{
\item{types}{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 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{Strauss()}.
}
\seealso{
\code{\link{ppm}},
\code{\link{pairwise.family}},
\code{\link{ppm.object}},
\code{\link{Strauss}}
}
\examples{
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))
# fit the stationary multitype Strauss process to `betacells'
ppm(betacells, ~polynom(x,y,3), MultiStrauss(c("off","on"), r))
# fit a nonstationary Strauss process with log-cubic polynomial trend
}
\section{Warnings}{
The argument \code{types} is interpreted as a
set of factor levels. That is,
in order that \code{\link{ppm}} can fit the multitype Strauss model
correctly to a point pattern \code{X},
this must be a marked point pattern; the mark vector
\code{X$marks} must be a factor; and
the argument \code{types} must
equal \code{levels(X$marks)}.
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{models}