# logLik.ppm

##### Log Likelihood and AIC for Point Process Model

Extracts the log likelihood and AIC of a fitted Poisson point process model, or analogous quantities based on the pseudolikelihood for a fitted Gibbs point process model.

##### Usage

```
## S3 method for class 'ppm':
logLik(object, ..., warn=TRUE)
## S3 method for class 'ppm':
extractAIC(fit, scale=0, k=2, \dots)
## S3 method for class '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 is returned instead of the likelihood. - 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 `"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
$$AIC = -2 \log(L) + k \times \mbox{edf}$$
where $L$ is the maximised likelihood of the fitted model,
and $\mbox{edf}$ is 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 (if `fit`

is a Gibbs model).

The method `nobs.ppm`

returns the number of points
in the original data point pattern to which the model was fitted.
The Rfunctions `AIC`

and `step`

use
these methods.

##### Value

- A numerical value.

##### 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

```
data(cells)
fit <- ppm(cells, ~x)
nobs(fit)
logLik(fit)
extractAIC(fit)
AIC(fit)
step(fit)
```

*Documentation reproduced from package spatstat, version 1.23-3, License: GPL (>= 2)*