logLik.ppm
Log Likelihood and AIC for Point Process Model
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.
Usage
# 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, …)
Arguments
- object,fit
Fitted point process model. An object of class
"ppm".- …
Ignored.
- warn
If
TRUE, a warning is given when the pseudolikelihood or logistic likelihood is returned instead of the likelihood.- absolute
Logical value indicating whether to include constant terms in the loglikelihood.
- scale
Ignored.
- k
Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.
- new.coef
New values for the canonical parameters of the model. A numeric vector of the same length as
coef(object).- takeuchi
Logical value specifying whether to use the Takeuchi penalty (
takeuchi=TRUE) or the number of fitted parameters (takeuchi=FALSE) in calculating AIC.
Details
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.
Value
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.
References
Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika 92, 519--528.
See Also
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.
Examples
# NOT RUN {
data(cells)
fit <- ppm(cells, ~x)
nobs(fit)
logLik(fit)
deviance(fit)
extractAIC(fit)
AIC(fit)
step(fit)
# }