Extracts the log likelihood, deviance, and AIC of a fitted Poisson point process model, or analogous quantities based on the pseudolikelihood or logistic likelihood for a fitted Gibbs point process model.
# S3 method for ppm
logLik(object, …, new.coef=NULL, warn=TRUE, absolute=FALSE)# S3 method for ppm
deviance(object, …)
# S3 method for ppm
AIC(object, …, k=2, takeuchi=TRUE)
# S3 method for ppm
extractAIC(fit, scale=0, k=2, …, takeuchi=TRUE)
# S3 method for ppm
nobs(object, …)
Fitted point process model.
An object of class "ppm".
Ignored.
If TRUE, a warning is given when the
pseudolikelihood or logistic likelihood
is returned instead of the likelihood.
Logical value indicating whether to include constant terms in the loglikelihood.
Ignored.
Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.
New values for the canonical parameters of the model.
A numeric vector of the same length as coef(object).
Logical value specifying whether to use the Takeuchi penalty
(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.
The values of logLik and AIC returned by these functions
are based on the pseudolikelihood of the Gibbs point process
model. If the model is a Poisson process, then the pseudolikelihood
is the same as the likelihood, but for other Gibbs models,
the pseudolikelihood is different from the likelihood (and the
likelihood of a Gibbs model is hard to compute).
For model comparison and model selection,
it is valid to compare the logLik values,
or to compare the AIC values, but only when
all the models are of class "ppm".
These functions are methods for the generic commands
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 \(\mbox{penalty}\) 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 \(\mbox{penalty}\) 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 R function step uses these methods.
Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika 92, 519--528.
ppm,
as.owin,
anova.ppm,
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.
# NOT RUN {
data(cells)
fit <- ppm(cells, ~x)
nobs(fit)
logLik(fit)
deviance(fit)
extractAIC(fit)
AIC(fit)
step(fit)
# }
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