Akaike Information Criterion for GKw Regression Models

Calculates the Akaike Information Criterion (AIC) for fitted Generalized Kumaraswamy regression models.

Usage

# S3 method for class 'gkwreg'
AIC(object, ..., k = 2)

Arguments

object: An object of class "gkwreg", typically obtained from gkwreg.
...: Optionally more fitted model objects.
k: Numeric, the penalty per parameter. Default is k = 2 for classical AIC. Setting k = log(n) gives BIC-equivalent penalty.

Value

If only one object is provided, returns a numeric value with the AIC. If multiple objects are provided, returns a data frame with columns df and AIC, with rows named according to the object names in the call.

Details

The AIC is computed as: $$AIC = -2\ell(\hat{\theta}) + k \cdot p$$ where $\ell(\hat{\theta})$ is the maximized log-likelihood and $p$ is the number of estimated parameters.

When multiple objects are provided, a data frame comparing all models is returned. Lower AIC values indicate better models, balancing goodness-of-fit against model complexity.

For small sample sizes, consider the corrected AIC (AICc): $$AICc = AIC + \frac{2p(p+1)}{n-p-1}$$ where $n$ is the sample size. This correction is not automatically applied but can be calculated manually.

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. doi:10.1109/TAC.1974.1100705

Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261–304. doi:10.1177/0049124104268644

Author

Lopes, J. E.

Examples

# \donttest{
# Load example data
data(GasolineYield)

# Fit competing models
fit1 <- gkwreg(yield ~ batch, data = GasolineYield, family = "kw")
#> using C++ compiler: ‘g++ (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0’
fit2 <- gkwreg(yield ~ batch + temp, data = GasolineYield, family = "kw")
#> Warning: NaNs produced
fit3 <- gkwreg(yield ~ temp, data = GasolineYield, family = "kw")

# Calculate AIC for single model
AIC(fit1)
#> [1] -42.93436

# Compare multiple models (with proper names)
AIC(fit1, fit2, fit3)
#>      df        AIC
#> fit1 11  -42.93436
#> fit2 12 -169.93865
#> fit3  3  -74.90259

# Use different penalty
AIC(fit1, k = 4)
#> [1] -20.93436
# }