# logLik.kppm

##### Log Likelihood and AIC for Fitted Cox or Cluster Point Process Model

Extracts the log Palm likelihood, deviance, and AIC of a fitted Cox or cluster point process model.

##### Usage

```
# 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, ...)
```

##### Arguments

- 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.

##### Details

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.

##### 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

Tanaka, U. and Ogata, Y. and Stoyan, D. (2008)
Parameter estimation and model selection for
Neyman-Scott point processes.
*Biometrical Journal* **50**, 43--57.

##### See Also

##### Examples

```
# NOT RUN {
fit <- kppm(redwood ~ x, "Thomas", method="palm")
nobs(fit)
logLik(fit)
extractAIC(fit)
AIC(fit)
step(fit)
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*