Compute AIC and AICc for one or several fitted model objects for which a log-likelihood value can be obtained.

## Usage

```
# S3 method for splm
AIC(object, ..., k = 2)
# S3 method for spautor
AIC(object, ..., k = 2)
# S3 method for spglm
AIC(object, ..., k = 2)
# S3 method for spgautor
AIC(object, ..., k = 2)
AICc(object, ..., k = 2)
# S3 method for splm
AICc(object, ..., k = 2)
# S3 method for spautor
AICc(object, ..., k = 2)
# S3 method for spglm
AICc(object, ..., k = 2)
# S3 method for spgautor
AICc(object, ..., k = 2)
```

## Arguments

- object
A fitted model object from

`splm()`

,`spautor()`

,`spglm()`

, or`spgautor()`

where`estmethod`

is`"ml"`

or`"reml"`

.- ...
Optionally more fitted model objects.

- k
The penalty parameter, taken to be 2. Currently not allowed to differ from 2 (needed for generic consistency).

## Value

If just one object is provided, a numeric value with the corresponding AIC or AICc.

If multiple objects are provided, a `data.frame`

with rows corresponding
to the objects and columns representing the number of parameters estimated
(`df`

) and the AIC or AICc.

## Details

When comparing models fit by maximum or restricted maximum
likelihood, the smaller the AIC or AICc, the better the fit. The AICc contains
a correction to AIC for small sample sizes. The theory of
AIC and AICc requires that the log-likelihood has been maximized, and hence,
no AIC or AICc methods exist for models where `estmethod`

is not
`"ml"`

or `"reml"`

. Additionally, AIC and AICc comparisons between `"ml"`

and `"reml"`

models are meaningless -- comparisons should only be made
within a set of models estimated using `"ml"`

or a set of models estimated
using `"reml"`

. AIC and AICc comparisons for `"reml"`

must
use the same fixed effects. To vary the covariance parameters and
fixed effects simultaneously, use `"ml"`

.

Hoeting et al. (2006) defines that spatial AIC as
\(-2loglik + 2(estparams)\) and the spatial AICc as
\(-2loglik + 2n(estparams) / (n - estparams - 1)\), where \(n\) is the sample size
and \(estparams\) is the number of estimated parameters. For `"ml"`

, \(estparams\) is
the number of estimated covariance parameters plus the number of estimated
fixed effects. For `"reml"`

, \(estparams\) is the number of estimated covariance
parameters.