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

## 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
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 AICc.

## Details

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

is not
`"ml"`

or `"reml"`

. Additionally, 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"`

. 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) study AIC and AICc in a spatial context, using the AIC definition
\(-2loglik + 2(estparams)\) and the AICc definition 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.

## Examples

```
spmod <- splm(z ~ water + tarp,
data = caribou,
spcov_type = "exponential", xcoord = x, ycoord = y
)
AICc(spmod)
#> [1] 1.073229
AIC(spmod)
#> [1] 0.1501516
BIC(spmod)
#> [1] 4.353744
```