"logLik"(object, ..., new.coef=NULL, warn=TRUE, absolute=FALSE)
"deviance"(object, ...)
"AIC"(object, ..., k=2, takeuchi=TRUE)
"extractAIC"(fit, scale=0, k=2, ..., takeuchi=TRUE)
"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,
deviance,
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 $penalty$ is a penalty for model complexity,
usually equal to 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 $penalty$ term is calculated
as follows. If takeuchi=FALSE then $penalty$ is
the number of fitted parameters. If takeuchi=TRUE then
$penalty = trace(J H^(-1))$
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 R function 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)
deviance(fit)
extractAIC(fit)
AIC(fit)
step(fit)
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