Compute the AIC or the second-order Akaike's information criterion (AICc).
`performance_aic()`

is a small wrapper that returns the AIC, however, for
models with a transformed response variable, `performance_aic()`

returns the
corrected AIC value (see 'Examples'). It is a generic function that also
works for some models that don't have a AIC method (like Tweedie models).
`performance_aicc()`

returns the second-order (or "small sample") AIC that
incorporates a correction for small sample sizes.

## Usage

```
performance_aicc(x, ...)
performance_aic(x, ...)
# S3 method for default
performance_aic(x, estimator = "ML", verbose = TRUE, ...)
# S3 method for lmerMod
performance_aic(x, estimator = "REML", verbose = TRUE, ...)
```

## Arguments

- x
A model object.

- ...
Currently not used.

- estimator
Only for linear models. Corresponds to the different estimators for the standard deviation of the errors. If

`estimator = "ML"`

(default, except for`performance_aic()`

when the model object is of class`lmerMod`

), the scaling is done by`n`

(the biased ML estimator), which is then equivalent to using`AIC(logLik())`

. Setting it to`"REML"`

will give the same results as`AIC(logLik(..., REML = TRUE))`

.- verbose
Toggle warnings.

## Details

`performance_aic()`

correctly detects transformed response and,
unlike `stats::AIC()`

, returns the "corrected" AIC value on the original
scale. To get back to the original scale, the likelihood of the model is
multiplied by the Jacobian/derivative of the transformation.

## References

Akaike, H. (1973) Information theory as an extension of the maximum likelihood principle. In: Second International Symposium on Information Theory, pp. 267-281. Petrov, B.N., Csaki, F., Eds, Akademiai Kiado, Budapest.

Hurvich, C. M., Tsai, C.-L. (1991) Bias of the corrected AIC criterion for underfitted regression and time series models. Biometrika 78, 499–509.

## Examples

```
m <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
AIC(m)
#> [1] 159.1051
performance_aicc(m)
#> [1] 162.4651
# correct AIC for models with transformed response variable
data("mtcars")
mtcars$mpg <- floor(mtcars$mpg)
model <- lm(log(mpg) ~ factor(cyl), mtcars)
# wrong AIC, not corrected for log-transformation
AIC(model)
#> [1] -19.67061
# performance_aic() correctly detects transformed response and
# returns corrected AIC
performance_aic(model)
#> [1] 168.2152
```