Extracts the log Palm likelihood, deviance, and AIC of a fitted Cox or cluster point process model.
# S3 method for kppm
logLik(object, ...)
# S3 method for kppm
AIC(object, …, k=2)
# S3 method for kppm
extractAIC(fit, scale=0, k=2, …)
# S3 method for kppm
nobs(object, ...)
Fitted point process model.
An object of class "kppm"
.
Ignored.
Ignored.
Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.
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 log-likelihood and AIC returned by these functions
are based on the Palm likelihood of the cluster process or Cox
process model. They are available only when the model was fitted
using method="palm"
. 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 "kppm"
and were fitted using method="palm"
.
These functions are methods for the generic commands
logLik
,
extractAIC
and
nobs
for the class "kppm"
.
An object of class "kppm"
represents a fitted
Cox or cluster point process model.
It is obtained from the model-fitting function kppm
.
These methods apply only when the model was fitted
by maximising the Palm likelihood (Tanaka et al, 2008)
by calling kppm
with the argument method="palm"
.
The method logLik.kppm
computes the
maximised value of the log Palm likelihood for the fitted model object
.
The methods AIC.kppm
and extractAIC.kppm
compute the
Akaike Information Criterion AIC for the fitted model
based on the Palm likelihood (Tanaka et al, 2008)
$$
AIC = -2 \log(PL) + k \times \mbox{edf}
$$
where \(PL\) is the maximised Palm likelihood of the fitted model,
and \(\mbox{edf}\) is the effective degrees of freedom
of the model.
The method nobs.kppm
returns the number of points
in the original data point pattern to which the model was fitted.
The R function step
uses these methods.
Tanaka, U. and Ogata, Y. and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal 50, 43--57.
# NOT RUN {
fit <- kppm(redwood ~ x, "Thomas", method="palm")
nobs(fit)
logLik(fit)
extractAIC(fit)
AIC(fit)
step(fit)
# }
Run the code above in your browser using DataCamp Workspace