Hybrid.Rd
\name{Hybrid}
\alias{Hybrid}
\title{
Hybrid Interaction Point Process Model
}
\description{
Creates an instance of a hybrid point process model
which can then be fitted to point pattern data.
}
\usage{
Hybrid(...)
}
\arguments{
\item{\dots}{
Two or more interactions (objects of class \code{"interact"})
or objects which can be converted to interactions.
See Details.
}
}
\details{
A \emph{hybrid} (Baddeley, Turner, Mateu and Bevan, 2013)
is a point process model created by combining two or more
point process models, or an interpoint interaction created by combining
two or more interpoint interactions.
The \emph{hybrid} of two point processes, with probability densities
\eqn{f(x)} and \eqn{g(x)} respectively,
is the point process with probability density
\deqn{h(x) = c \, f(x) \, g(x)}{h(x) = c * f(x) * g(x)}
where \eqn{c} is a normalising constant.
Equivalently, the hybrid of two point processes with conditional intensities
\eqn{\lambda(u,x)}{lambda(u,x)} and \eqn{\kappa(u,x)}{kappa(u,x)}
is the point process with conditional intensity
\deqn{
\phi(u,x) = \lambda(u,x) \, \kappa(u,x).
}{
phi(u,x) = lambda(u,x) * kappa(u,x).
}
The hybrid of \eqn{m > 3} point processes is defined in a similar way.
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 a hybrid interaction is
yielded by the function \code{Hybrid()}.
The arguments \code{\dots} will be interpreted as interpoint interactions
(objects of class \code{"interact"}) and the result will be the hybrid
of these interactions. Each argument must either be an
interpoint interaction (object of class \code{"interact"}),
or a point process model (object of class \code{"ppm"}) from which the
interpoint interaction will be extracted.
The arguments \code{\dots} may also be given in the form
\code{name=value}. This is purely cosmetic: it can be used to attach
simple mnemonic names to the component interactions, and makes the
printed output from \code{\link{print.ppm}} neater.
}
\value{
An object of class \code{"interact"}
describing an interpoint interaction structure.
}
\references{
Baddeley, A., Turner, R., Mateu, J. and Bevan, A. (2013)
Hybrids of Gibbs point process models and their implementation.
\emph{Journal of Statistical Software} \bold{55}:11, 1--43.
\url{http://www.jstatsoft.org/v55/i11/}
}
\seealso{
\code{\link{ppm}}
}
\examples{
Hybrid(Strauss(0.1), Geyer(0.2, 3))
Hybrid(Ha=Hardcore(0.05), St=Strauss(0.1), Ge=Geyer(0.2, 3))
fit <- ppm(redwood, ~1, Hybrid(A=Strauss(0.02), B=Geyer(0.1, 2)))
fit
ctr <- rmhcontrol(nrep=5e4, expand=1)
plot(simulate(fit, control=ctr))
# hybrid components can be models (including hybrid models)
Hybrid(fit, S=Softcore(0.5))
# plot.fii only works if every component is a pairwise interaction
data(swedishpines)
fit2 <- ppm(swedishpines, ~1, Hybrid(DG=DiggleGratton(2,10), S=Strauss(5)))
plot(fitin(fit2))
plot(fitin(fit2), separate=TRUE, mar.panel=rep(4,4))
}
\author{\adrian
and \rolf
}
\keyword{spatial}
\keyword{models}