https://github.com/cran/spatstat
Tip revision: 32c7daeb36b6e48fd0356bdcec9580ae124fee5e authored by Adrian Baddeley on 29 December 2015, 22:08:27 UTC
version 1.44-1
version 1.44-1
Tip revision: 32c7dae
vargamma.estK.Rd
\name{vargamma.estK}
\alias{vargamma.estK}
\title{Fit the Neyman-Scott Cluster Point Process with Variance Gamma kernel}
\description{
Fits the Neyman-Scott cluster point process, with Variance Gamma
kernel, to a point pattern dataset by the Method of Minimum Contrast.
}
\usage{
vargamma.estK(X, startpar=c(kappa=1,scale=1), nu = -1/4, lambda=NULL,
q = 1/4, p = 2, rmin = NULL, rmax = NULL, ...)
}
\arguments{
\item{X}{
Data to which the model will be fitted.
Either a point pattern or a summary statistic.
See Details.
}
\item{startpar}{
Vector of starting values for the parameters of the model.
}
\item{nu}{
Numerical value controlling the shape of the tail of the clusters.
A number greater than \code{-1/2}.
}
\item{lambda}{
Optional. An estimate of the intensity of the point process.
}
\item{q,p}{
Optional. Exponents for the contrast criterion.
}
\item{rmin, rmax}{
Optional. The interval of \eqn{r} values for the contrast criterion.
}
\item{\dots}{
Optional arguments passed to \code{\link[stats]{optim}}
to control the optimisation algorithm. See Details.
}
}
\details{
This algorithm fits the Neyman-Scott Cluster point process model
with Variance Gamma kernel (Jalilian et al, 2013)
to a point pattern dataset
by the Method of Minimum Contrast, using the \eqn{K} function.
The argument \code{X} can be either
\describe{
\item{a point pattern:}{An object of class \code{"ppp"}
representing a point pattern dataset.
The \eqn{K} function of the point pattern will be computed
using \code{\link{Kest}}, and the method of minimum contrast
will be applied to this.
}
\item{a summary statistic:}{An object of class \code{"fv"} containing
the values of a summary statistic, computed for a point pattern
dataset. The summary statistic should be the \eqn{K} function,
and this object should have been obtained by a call to
\code{\link{Kest}} or one of its relatives.
}
}
The algorithm fits the Neyman-Scott Cluster point process
with Variance Gamma kernel to \code{X},
by finding the parameters of the model
which give the closest match between the
theoretical \eqn{K} function of the model
and the observed \eqn{K} function.
For a more detailed explanation of the Method of Minimum Contrast,
see \code{\link{mincontrast}}.
The Neyman-Scott cluster point process with Variance Gamma
kernel is described in Jalilian et al (2013).
It is a cluster process formed by taking a
pattern of parent points, generated according to a Poisson process
with intensity \eqn{\kappa}{kappa}, and around each parent point,
generating a random number of offspring points, such that the
number of offspring of each parent is a Poisson random variable with mean
\eqn{\mu}{mu}, and the locations of the offspring points of one parent
have a common distribution described in Jalilian et al (2013).
The shape of the kernel is determined by the dimensionless
index \code{nu}. This is the parameter
\eqn{\nu^\prime = \alpha/2-1}{nu' = alpha/2 - 1} appearing in
equation (12) on page 126 of Jalilian et al (2013).
In previous versions of spatstat instead of specifying \code{nu}
(called \code{nu.ker} at that time) the user could specify
\code{nu.pcf} which is the parameter \eqn{\nu=\alpha-1}{nu = alpha-1}
appearing in equation (13), page 127 of Jalilian et al (2013).
These are related by \code{nu.pcf = 2 * nu.ker + 1}
and \code{nu.ker = (nu.pcf - 1)/2}. This syntax is still supported but
not recommended for consistency across the package. In that case
exactly one of \code{nu.ker} or \code{nu.pcf} must be specified.
If the argument \code{lambda} is provided, then this is used
as the value of the point process intensity \eqn{\lambda}{lambda}.
Otherwise, if \code{X} is a
point pattern, then \eqn{\lambda}{lambda}
will be estimated from \code{X}.
If \code{X} is a summary statistic and \code{lambda} is missing,
then the intensity \eqn{\lambda}{lambda} cannot be estimated, and
the parameter \eqn{\mu}{mu} will be returned as \code{NA}.
The remaining arguments \code{rmin,rmax,q,p} control the
method of minimum contrast; see \code{\link{mincontrast}}.
The corresponding model can be simulated using \code{\link{rVarGamma}}.
The parameter \code{eta} appearing in \code{startpar} is equivalent to the
scale parameter \code{omega} used in \code{\link{rVarGamma}}.
Homogeneous or inhomogeneous Neyman-Scott/VarGamma models can also be
fitted using the function \code{\link{kppm}} and the fitted models
can be simulated using \code{\link{simulate.kppm}}.
The optimisation algorithm can be controlled through the
additional arguments \code{"..."} which are passed to the
optimisation function \code{\link[stats]{optim}}. For example,
to constrain the parameter values to a certain range,
use the argument \code{method="L-BFGS-B"} to select an optimisation
algorithm that respects box constraints, and use the arguments
\code{lower} and \code{upper} to specify (vectors of) minimum and
maximum values for each parameter.
}
\value{
An object of class \code{"minconfit"}. There are methods for printing
and plotting this object. It contains the following main components:
\item{par }{Vector of fitted parameter values.}
\item{fit }{Function value table (object of class \code{"fv"})
containing the observed values of the summary statistic
(\code{observed}) and the theoretical values of the summary
statistic computed from the fitted model parameters.
}
}
\references{
Jalilian, A., Guan, Y. and Waagepetersen, R. (2013)
Decomposition of variance for spatial Cox processes.
\emph{Scandinavian Journal of Statistics} \bold{40}, 119-137.
Waagepetersen, R. (2007)
An estimating function approach to inference for
inhomogeneous Neyman-Scott processes.
\emph{Biometrics} \bold{63}, 252--258.
}
\author{Abdollah Jalilian and Rasmus Waagepetersen.
Adapted for \pkg{spatstat} by Adrian Baddeley \email{Adrian.Baddeley@curtin.edu.au}
}
\seealso{
\code{\link{kppm}},
\code{\link{vargamma.estpcf}},
\code{\link{lgcp.estK}},
\code{\link{thomas.estK}},
\code{\link{cauchy.estK}},
\code{\link{mincontrast}},
\code{\link{Kest}},
\code{\link{Kmodel}}.
\code{\link{rVarGamma}} to simulate the model.
}
\examples{
\testonly{
u <- vargamma.estK(redwood, startpar=c(kappa=15, eta=0.075))
}
if(interactive()) {
u <- vargamma.estK(redwood)
u
plot(u)
}
}
\keyword{spatial}
\keyword{models}