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\name{linearKdot.inhom}
\alias{linearKdot.inhom}
\title{
Inhomogeneous multitype K Function (Dot-type) for Linear Point Pattern
}
\description{
For a multitype point pattern on a linear network,
estimate the inhomogeneous multitype \eqn{K} function
which counts the expected number of points (of any type)
within a given distance of a point of type \eqn{i}.
}
\usage{
linearKdot.inhom(X, i, lambdaI=NULL, lambdadot=NULL, r=NULL, \dots,
correction="Ang", normalise=TRUE, sigma=NULL)
}
\arguments{
\item{X}{The observed point pattern,
from which an estimate of the dot type \eqn{K} function
\eqn{K_{i\bullet}(r)}{K[i.](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{lambdaI}{
Intensity values for the points of type \code{i}. Either a numeric vector,
a \code{function}, a pixel image
(object of class \code{"im"} or \code{"linim"}) or
a fitted point process model (object of class \code{"ppm"}
or \code{"lppm"}) or \code{NULL}.
}
\item{lambdadot}{
Intensity values for all points of \code{X}. Either a numeric vector,
a \code{function}, a pixel image
(object of class \code{"im"} or \code{"linim"}) or
a fitted point process model (object of class \code{"ppm"}
or \code{"lppm"}) or \code{NULL}.
}
\item{r}{numeric vector. The values of the argument \eqn{r}
at which the \eqn{K}-function
\eqn{K_{i\bullet}(r)}{K[i.](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}{
Arguments passed to \code{lambdaI} and \code{lambdadot} if
they are functions.
}
\item{normalise}{
Logical. If \code{TRUE} (the default), the denominator of the estimator is
data-dependent (equal to the sum of the reciprocal intensities at
the points of type \code{i}), which reduces the sampling variability.
If \code{FALSE}, the denominator is the length of the network.
}
\item{sigma}{
Smoothing bandwidth passed to \code{\link{density.lpp}}
for estimation of intensities when either \code{lambdaI} or
\code{lambdadot} is \code{NULL}.
}
}
\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]{Kdot.inhom}}
for a point pattern on a linear network (object of class \code{"lpp"}).
The argument \code{i} will be interpreted as
levels of the factor \code{marks(X)}.
If \code{i} is missing, it defaults to the first
level of the marks factor.
The argument \code{r} is the vector of values for the
distance \eqn{r} at which \eqn{K_{i\bullet}(r)}{Ki.(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.
If \code{lambdaI} or \code{lambdadot} is missing, it will be estimated
by kernel smoothing using \code{\link{density.lpp}}.
If \code{lambdaI} or \code{lambdadot} is a fitted point process model,
the default behaviour is to update the model by re-fitting it to
the data, before computing the fitted intensity.
This can be disabled by setting \code{update=FALSE}.
}
\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 argument \code{i} is interpreted as a
level 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{
lam <- table(marks(chicago))/(summary(chicago)$totlength)
lamI <- function(x,y,const=lam[["assault"]]){ rep(const, length(x)) }
lam. <- function(x,y,const=sum(lam)){ rep(const, length(x)) }
K <- linearKdot.inhom(chicago, "assault", lamI, lam.)
# using fitted models for the intensity
# fit <- lppm(chicago ~marks + x)
# linearKdot.inhom(chicago, "assault", fit, fit)
}
\author{\adrian
}
\keyword{spatial}
\keyword{nonparametric}
\concept{Linear network}
|
