DiggleGatesStibbard.Rd
\name{DiggleGatesStibbard}
\alias{DiggleGatesStibbard}
\title{Diggle-Gates-Stibbard Point Process Model}
\description{
Creates an instance of the Diggle-Gates-Stibbard point process model
which can then be fitted to point pattern data.
}
\usage{
DiggleGatesStibbard(rho)
}
\arguments{
\item{rho}{Interaction range}
}
\value{
An object of class \code{"interact"}
describing the interpoint interaction
structure of the Diggle-Gates-Stibbard
process with interaction range \code{rho}.
}
\details{
Diggle, Gates and Stibbard (1987) proposed a pairwise interaction
point process in which each pair of points separated by
a distance \eqn{d} contributes a factor \eqn{e(d)} to the
probability density, where
\deqn{
e(d) = \sin^2\left(\frac{\pi d}{2\rho}\right)
}{
e(d) = sin^2((pi * d)/(2 * rho))
}
for \eqn{d < \rho}{d < rho}, and \eqn{e(d)} is equal to 1
for \eqn{d \ge \rho}{d >= rho}.
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 Diggle-Gates-Stibbard
pairwise interaction is
yielded by the function \code{DiggleGatesStibbard()}.
See the examples below.
Note that this model does not have any regular parameters
(as explained in the section on Interaction Parameters
in the help file for \code{\link{ppm}}).
The parameter \eqn{rho} is not estimated by \code{\link{ppm}}.
}
\seealso{
\code{\link{ppm}},
\code{\link{pairwise.family}},
\code{\link{DiggleGratton}},
\code{\link{rDGS}},
\code{\link{ppm.object}}
}
\references{
Baddeley, A. and Turner, R. (2000)
Practical maximum pseudolikelihood for spatial point patterns.
\emph{Australian and New Zealand Journal of Statistics}
\bold{42}, 283--322.
Ripley, B.D. (1981)
\emph{Spatial statistics}.
John Wiley and Sons.
Diggle, P.J., Gates, D.J., and Stibbard, A. (1987)
A nonparametric estimator for pairwise-interaction point processes.
Biometrika \bold{74}, 763 -- 770.
\emph{Scandinavian Journal of Statistics} \bold{21}, 359--373.
}
\examples{
DiggleGatesStibbard(0.02)
# prints a sensible description of itself
data(cells)
\dontrun{
ppm(cells, ~1, DiggleGatesStibbard(0.05))
# fit the stationary D-G-S process to `cells'
}
ppm(cells, ~ polynom(x,y,3), DiggleGatesStibbard(0.05))
# fit a nonstationary D-G-S process
# with log-cubic polynomial trend
}
\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}