Pairwise.Rd
\name{Pairwise}
\alias{Pairwise}
\title{Generic Pairwise Interaction model}
\description{
Creates an instance of a pairwise interaction point process model
which can then be fitted to point pattern data.
}
\usage{
Pairwise(pot, name, par, parnames, printfun)
}
\arguments{
\item{pot}{An R language function giving the user-supplied
pairwise interaction potential.}
\item{name}{Character string.}
\item{par}{List of numerical values for irregular parameters}
\item{parnames}{Vector of names of irregular parameters}
\item{printfun}{Do not specify this argument: for internal use only.}
}
\value{
An object of class \code{"interact"}
describing the interpoint interaction
structure of a point process.
}
\details{
This code constructs a member of the
pairwise interaction family \code{\link{pairwise.family}}
with arbitrary pairwise interaction potential given by
the user.
Each pair of points in the point pattern contributes a factor
\eqn{h(d)} to the probability density, where \eqn{d} is the distance
between the two points. The factor term \eqn{h(d)} is
\deqn{h(d) = \exp(-\theta \mbox{pot}(d))}{h(d) = exp(-theta * pot(d))}
provided \eqn{\mbox{pot}(d)}{pot(d)} is finite,
where \eqn{\theta}{theta} is the coefficient vector in the model.
The function \code{pot} must take as its first argument
a matrix of interpoint distances, and evaluate the
potential for each of these distances. The result must be
either a matrix with the same dimensions as its input,
or an array with its first two dimensions the same as its input
(the latter case corresponds to a vector-valued potential).
If irregular parameters are present, then the second argument
to \code{pot} should be a vector of the same type as \code{par}
giving those parameter values.
The values returned by \code{pot} may be finite numeric values,
or \code{-Inf} indicating a hard core (that is, the corresponding
interpoint distance is forbidden). We define
\eqn{h(d) = 0} if \eqn{\mbox{pot}(d) = -\infty}{pot(d) = -Inf}.
Thus, a potential value of minus infinity is \emph{always} interpreted
as corresponding to \eqn{h(d) = 0}, regardless of the sign
and magnitude of \eqn{\theta}{theta}.
}
\seealso{
\code{\link{ppm}},
\code{\link{pairwise.family}},
\code{\link{ppm.object}}
}
\examples{
#This is the same as StraussHard(r=0.7,h=0.05)
strpot <- function(d,par) {
r <- par$r
h <- par$h
value <- (d <= r)
value[d < h] <- -Inf
value
}
mySH <- Pairwise(strpot, "StraussHard process", list(r=0.7,h=0.05),
c("interaction distance r", "hard core distance h"))
data(cells)
ppm(cells, ~ 1, mySH, correction="isotropic")
# Fiksel (1984) double exponential interaction
# see Stoyan, Kendall, Mecke 1987 p 161
fikspot <- function(d, par) {
r <- par$r
h <- par$h
zeta <- par$zeta
value <- exp(-zeta * d)
value[d < h] <- -Inf
value[d > r] <- 0
value
}
Fiksel <- Pairwise(fikspot, "Fiksel double exponential process",
list(r=3.5, h=1, zeta=1),
c("interaction distance r",
"hard core distance h",
"exponential coefficient zeta"))
data(spruces)
fit <- ppm(unmark(spruces), ~1, Fiksel, rbord=3.5)
fit
plot(fitin(fit), xlim=c(0,4))
coef(fit)
# corresponding values obtained by Fiksel (1984) were -1.9 and -6.0
}
\author{\adrian
and \rolf
}
\keyword{spatial}
\keyword{models}