## S3 method for class 'ppm':
logLik(object, ..., new.coef=NULL, warn=TRUE)
## S3 method for class 'ppm':
AIC(object, \dots, k=2, takeuchi=TRUE)
## S3 method for class 'ppm':
extractAIC(fit, scale=0, k=2, \dots, takeuchi=TRUE)
## S3 method for class 'ppm':
nobs(object, ...)
"ppm"
.TRUE
, a warning is given when the
pseudolikelihood or logistic likelihood
is returned instead of the likelihood.coef(object)
.takeuchi=TRUE
) or the
number of fitted parameters (takeuchi=FALSE
)
in calculating AIC.logLik
returns a numerical value, belonging to the class
"logLik"
, with an attribute "df"
giving the degrees of
freedom.
AIC
returns a numerical value. extractAIC
returns a numeric vector of length 2
containing the degrees of freedom and the AIC value.
nobs
returns an integer value.
logLik
,
extractAIC
and
nobs
for the class "ppm"
. An object of class "ppm"
represents a fitted
Poisson or Gibbs point process model.
It is obtained from the model-fitting function ppm
.
The method logLik.ppm
computes the
maximised value of the log likelihood for the fitted model object
(as approximated by quadrature using the Berman-Turner approximation)
is extracted. If object
is not a Poisson process, the maximised log
pseudolikelihood is returned, with a warning (if warn=TRUE
).
The Akaike Information Criterion AIC for a fitted model is defined as
$$AIC = -2 \log(L) + k \times \mbox{penalty}$$
where $L$ is the maximised likelihood of the fitted model,
and $\mbox{edf}$ is the effective degrees of freedom
of the model.
The method extractAIC.ppm
returns the analogous quantity
$AIC*$ in which $L$ is replaced by $L*$,
the quadrature approximation
to the likelihood (if fit
is a Poisson model)
or the pseudolikelihood or logistic likelihood
(if fit
is a Gibbs model).
The $\mbox{penalty}$ term is calculated
as follows. If takeuchi=FALSE
then $\mbox{penalty}$ is
the number of fitted parameters. If takeuchi=TRUE
then
$\mbox{penalty} = \mbox{trace}(J H^{-1})$
where $J$ and $H$ are the estimated variance and hessian,
respectively, of the composite score.
These two choices are equivalent for a Poisson process.
The method nobs.ppm
returns the number of points
in the original data point pattern to which the model was fitted.
The Rfunction step
uses these methods.
ppm
,
as.owin
,
coef.ppm
,
fitted.ppm
,
formula.ppm
,
model.frame.ppm
,
model.matrix.ppm
,
plot.ppm
,
predict.ppm
,
residuals.ppm
,
simulate.ppm
,
summary.ppm
,
terms.ppm
,
update.ppm
,
vcov.ppm
.data(cells)
fit <- ppm(cells, ~x)
nobs(fit)
logLik(fit)
extractAIC(fit)
AIC(fit)
step(fit)
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