\name{Kres}
\Rdversion{1.1}
\alias{Kres}
\title{
Residual K Function
}
\description{
Given a point process model fitted to a point pattern dataset,
this function computes the residual \eqn{K} function,
which serves as a diagnostic for goodness-of-fit of the model.
}
\usage{
Kres(object, ...)
}
\arguments{
\item{object}{
Object to be analysed.
Either a fitted point process model (object of class \code{"ppm"}),
a point pattern (object of class \code{"ppp"}),
a quadrature scheme (object of class \code{"quad"}),
or the value returned by a previous call to \code{\link{Kcom}}.
}
\item{\dots}{
Arguments passed to \code{\link{Kcom}}.
}
}
\details{
This command provides a diagnostic for the goodness-of-fit of
a point process model fitted to a point pattern dataset.
It computes a residual version of the \eqn{K} function of the
dataset, which should be approximately zero if the model is a good
fit to the data.
In normal use, \code{object} is a fitted point process model
or a point pattern. Then \code{Kres} first calls \code{\link{Kcom}}
to compute both the nonparametric estimate of the \eqn{K} function
and its model compensator. Then \code{Kres} computes the
difference between them, which is the residual \eqn{K}-function.
Alternatively, \code{object} may be a function value table
(object of class \code{"fv"}) that was returned by
a previous call to \code{\link{Kcom}}. Then \code{Kres} computes the
residual from this object.
}
\value{
A function value table (object of class \code{"fv"}),
essentially a data frame of function values.
There is a plot method for this class. See \code{\link{fv.object}}.
}
\references{
Baddeley, A., Rubak, E. and \ifelse{latex}{\out{M\o ller}}{Moller}, J. (2011)
Score, pseudo-score and residual
diagnostics for spatial point process models.
\emph{Statistical Science} \bold{26}, 613--646.
}
\author{
\adrian
\ege and Jesper \ifelse{latex}{\out{M\o ller}}{Moller}.
}
\seealso{
Related functions:
\code{\link{Kcom}},
\code{\link{Kest}}.
Alternative functions:
\code{\link{Gres}},
\code{\link{psstG}}, \code{\link{psstA}}, \code{\link{psst}}.
Point process models: \code{\link{ppm}}.
}
\examples{
data(cells)
fit0 <- ppm(cells, ~1) # uniform Poisson
\testonly{ fit0 <- ppm(cells, ~1, nd=16)}
K0 <- Kres(fit0)
K0
plot(K0)
# isotropic-correction estimate
plot(K0, ires ~ r)
# uniform Poisson is clearly not correct
fit1 <- ppm(cells, ~1, Strauss(0.08))
\testonly{fit1 <- ppm(cells, ~1, Strauss(0.08), nd=16)}
K1 <- Kres(fit1)
if(interactive()) {
plot(K1, ires ~ r)
# fit looks approximately OK; try adjusting interaction distance
plot(Kres(cells, interaction=Strauss(0.12)))
}
# How to make envelopes
\dontrun{
E <- envelope(fit1, Kres, model=fit1, nsim=19)
plot(E)
}
# For computational efficiency
Kc <- Kcom(fit1)
K1 <- Kres(Kc)
}
\keyword{spatial}
\keyword{models}