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Compute the AIC or second-order AIC

Source: R/performance_aicc.R
performance_aicc.Rd

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, ...)

# Default S3 method
performance_aic(x, estimator = "ML", verbose = TRUE, ...)

# S3 method for class '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.

Value

Numeric, the AIC or AICc value.

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.

In case it is not possible to return the corrected AIC value, a warning is given that the corrected log-likelihood value could not be computed.

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

# \dontrun{
# there are a few exceptions where the corrected log-likelihood values
# cannot be returned. The following exampe gives a warning.
model <- lm(1 / mpg ~ factor(cyl), mtcars)
performance_aic(model)
#> Warning: Could not compute corrected log-likelihood for models with transformed
#>   response. Log-likelihood value is probably inaccurate.
#> [1] -196.3387
# }