Extracts the log composite 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, ...)
```

object,fit

Fitted point process model.
An object of class `"kppm"`

.

…

Ignored.

scale

Ignored.

k

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 *composite likelihood* of the cluster process or Cox
process model. They are available only when the model was fitted
using `method="palm"`

or `method="clik2"`

.

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 the same `method`

.

For `method="palm"`

some theoretical justification was provided by
Tanaka et al (2008).

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 a composite likelihood:
either the Palm likelihood (Tanaka et al, 2008)
or the second order composite likelihood (Guan, 2006),
by calling `kppm`

with the argument `method="palm"`

or `method="clik2"`

respectively.

The method `logLik.kppm`

computes the
maximised value of the log composite 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 composite likelihood
$$
AIC = -2 \log(CL) + k \times \mbox{edf}
$$
where \(CL\) is the maximised composite 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.

Guan, Y. (2006)
A composite likelihood approach in fitting spatial point process
models.
*Journal of the American Statistical Association*
**101**, 1502--1512.

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) # }