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\name{linearKcross}
\alias{linearKcross}
\title{
Multitype K Function (Cross-type) for Linear Point Pattern
}
\description{
For a multitype point pattern on a linear network,
estimate the multitype \eqn{K} function
which counts the expected number of points of type \eqn{j}
within a given distance of a point of type \eqn{i}.
}
\usage{
linearKcross(X, i, j, r=NULL, \dots, correction="Ang")
}
\arguments{
\item{X}{The observed point pattern,
from which an estimate of the cross type \eqn{K} function
\eqn{K_{ij}(r)}{Kij(r)} will be computed.
An object of class \code{"lpp"} which
must be a multitype point pattern (a marked point pattern
whose marks are a factor).
}
\item{i}{Number or character string identifying the type (mark value)
of the points in \code{X} from which distances are measured.
Defaults to the first level of \code{marks(X)}.
}
\item{j}{Number or character string identifying the type (mark value)
of the points in \code{X} to which distances are measured.
Defaults to the second level of \code{marks(X)}.
}
\item{r}{numeric vector. The values of the argument \eqn{r}
at which the \eqn{K}-function
\eqn{K_{ij}(r)}{Kij(r)} should be evaluated.
There is a sensible default.
First-time users are strongly advised not to specify this argument.
See below for important conditions on \eqn{r}.
}
\item{correction}{
Geometry correction.
Either \code{"none"} or \code{"Ang"}. See Details.
}
\item{\dots}{Ignored.}
}
\value{
An object of class \code{"fv"} (see \code{\link[spatstat.explore]{fv.object}}).
}
\details{
This is a counterpart of the function \code{\link[spatstat.explore]{Kcross}}
for a point pattern on a linear network (object of class \code{"lpp"}).
The arguments \code{i} and \code{j} will be interpreted as
levels of the factor \code{marks(X)}.
If \code{i} and \code{j} are missing, they default to the first
and second level of the marks factor, respectively.
The argument \code{r} is the vector of values for the
distance \eqn{r} at which \eqn{K_{ij}(r)}{Kij(r)} should be evaluated.
The values of \eqn{r} must be increasing nonnegative numbers
and the maximum \eqn{r} value must not exceed the radius of the
largest disc contained in the window.
}
\references{
Baddeley, A, Jammalamadaka, A. and Nair, G. (2014)
Multitype point process analysis of spines on the
dendrite network of a neuron.
\emph{Applied Statistics} (Journal of the Royal Statistical
Society, Series C), \bold{63}, 673--694.
}
\section{Warnings}{
The arguments \code{i} and \code{j} are interpreted as
levels of the factor \code{marks(X)}. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values.
}
\seealso{
\code{\link{linearKdot}},
\code{\link{linearK}}.
}
\examples{
K <- linearKcross(chicago, "assault", "robbery")
}
\author{\adrian
}
\keyword{spatial}
\keyword{nonparametric}
\concept{Linear network}
|
