Bayesian Information Criterion for GKw Regression Models

Calculates the Bayesian Information Criterion (BIC), also known as the Schwarz Information Criterion (SIC), for fitted Generalized Kumaraswamy regression models.

Usage

# S3 method for class 'gkwreg'
BIC(object, ...)

Arguments

object: An object of class "gkwreg", typically obtained from gkwreg.
...: Optionally more fitted model objects.

Value

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

Details

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

When multiple objects are provided, a data frame comparing all models is returned. Lower BIC values indicate better models. BIC penalizes model complexity more heavily than AIC, particularly for large samples, and tends to favor more parsimonious models.

The BIC can be derived from a Bayesian perspective as an approximation to the logarithm of the Bayes factor, under certain regularity conditions and assuming uniform priors.

References

Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. doi:10.1214/aos/1176344136

Author

Lopes, J. E.

Examples

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

# Fit competing models
fit1 <- gkwreg(yield ~ batch, data = GasolineYield, family = "kw")
fit2 <- gkwreg(yield ~ batch + temp, data = GasolineYield, family = "kw")
#> Warning: NaNs produced
fit3 <- gkwreg(yield ~ temp, data = GasolineYield, family = "kw")

# Calculate BIC for single model
BIC(fit1)
#> [1] -26.81126

# Compare multiple models (with proper names)
BIC(fit1, fit2, fit3)
#>      df        BIC
#> fit1 11  -26.81126
#> fit2 12 -152.34982
#> fit3  3  -70.50538
# }