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
logLik.mppm.Rd
\name{logLik.mppm}
\alias{logLik.mppm}
\alias{AIC.mppm}
\alias{extractAIC.mppm}
\alias{nobs.mppm}
\alias{getCall.mppm}
\alias{terms.mppm}
\title{Log Likelihood and AIC for Multiple Point Process Model}
\description{
For a point process model that has been fitted to multiple point
patterns, these functions extract the log likelihood and AIC,
or analogous quantities based on the pseudolikelihood.
}
\usage{
\method{logLik}{mppm}(object, \dots, warn=TRUE)
\method{AIC}{mppm}(object, \dots, k=2, takeuchi=TRUE)
\method{extractAIC}{mppm}(fit, scale = 0, k = 2, \dots, takeuchi = TRUE)
\method{nobs}{mppm}(object, \dots)
\method{getCall}{mppm}(x, \dots)
\method{terms}{mppm}(x, \dots)
}
\arguments{
\item{object,fit,x}{
Fitted point process model (fitted to multiple point
patterns). An object of class \code{"mppm"}.
}
\item{\dots}{Ignored.}
\item{warn}{
If \code{TRUE}, a warning is given when the
pseudolikelihood is returned instead of the likelihood.
}
\item{scale}{Ignored.}
\item{k}{Numeric value specifying the weight of the
equivalent degrees of freedom in the AIC. See Details.
}
\item{takeuchi}{
Logical value specifying whether to use the Takeuchi penalty
(\code{takeuchi=TRUE}) or the
number of fitted parameters (\code{takeuchi=FALSE})
in calculating AIC.
}
}
\details{
These functions are methods for the generic commands
\code{\link[stats]{logLik}},
\code{\link[stats]{AIC}},
\code{\link[stats]{extractAIC}},
\code{\link[stats]{terms}} and
\code{\link[stats:update]{getCall}}
for the class \code{"mppm"}.
An object of class \code{"mppm"} represents a fitted
Poisson or Gibbs point process model fitted to several point patterns.
It is obtained from the model-fitting function \code{\link{mppm}}.
The method \code{logLik.mppm} extracts the
maximised value of the log likelihood for the fitted model
(as approximated by quadrature using the Berman-Turner approximation).
If \code{object} is not a Poisson process, the maximised log
\emph{pseudolikelihood} is returned, with a warning.
The Akaike Information Criterion AIC for a fitted model is defined as
\deqn{
AIC = -2 \log(L) + k \times \mbox{penalty}
}{
AIC = -2 * log(L) + k * penalty
}
where \eqn{L} is the maximised likelihood of the fitted model,
and \eqn{\mbox{penalty}}{penalty} is a penalty for model complexity,
usually equal to the effective degrees of freedom of the model.
The method \code{extractAIC.mppm} returns the \emph{analogous} quantity
\eqn{AIC*} in which \eqn{L} is replaced by \eqn{L*},
the quadrature approximation
to the likelihood (if \code{fit} is a Poisson model)
or the pseudolikelihood (if \code{fit} is a Gibbs model).
The \eqn{\mbox{penalty}}{penalty} term is calculated
as follows. If \code{takeuchi=FALSE} then \eqn{\mbox{penalty}}{penalty} is
the number of fitted parameters. If \code{takeuchi=TRUE} then
\eqn{\mbox{penalty} = \mbox{trace}(J H^{-1})}{penalty = trace(J H^(-1))}
where \eqn{J} and \eqn{H} are the estimated variance and hessian,
respectively, of the composite score.
These two choices are equivalent for a Poisson process.
The method \code{nobs.mppm} returns the total number of points
in the original data point patterns to which the model was fitted.
The method \code{getCall.mppm} extracts the original call to
\code{\link{mppm}} which caused the model to be fitted.
The method \code{terms.mppm} extracts the covariate terms in the
model formula as a \code{terms} object. Note that these terms do not
include the interaction component of the model.
The \R function \code{\link[stats]{step}} uses these methods.
}
\value{
See the help files for the corresponding generic functions.
}
\seealso{
\code{\link{mppm}}
}
\references{
Baddeley, A., Rubak, E. and Turner, R. (2015)
\emph{Spatial Point Patterns: Methodology and Applications with R}.
London: Chapman and Hall/CRC Press.
}
\author{
Adrian Baddeley, Ida-Maria Sintorn and Leanne Bischoff.
Implemented by
Adrian Baddeley \email{Adrian.Baddeley@curtin.edu.au},
Rolf Turner \email{r.turner@auckland.ac.nz}
and Ege Rubak \email{rubak@math.aau.dk}.
}
\examples{
fit <- mppm(Bugs ~ x, hyperframe(Bugs=waterstriders))
logLik(fit)
AIC(fit)
nobs(fit)
getCall(fit)
}
\keyword{spatial}
\keyword{models}