AIC {base}

R Documentation

Akaike Information Criterion

Description

Generic function calculating the Akaike information criterion for one or several fitted model objects for which a log-likelihood value can be obtained, according to the formula -2 \mbox{log-likelihood} + k n_{par}, where n_{par} represents the number of parameters in the fitted model, and k = 2 for the usual AIC, or k = \log(n) (n the number of observations) for the so-called BIC or SBC (Schwarz's Bayesian criterion).

Usage

AIC(object, ..., k = 2)

Arguments

object	a fitted model object, for which there exists a logLik method to extract the corresponding log-likelihood, or an object inheriting from class logLik.
...	optionally more fitted model objects.
k	numeric, the “penalty” per parameter to be used; the default k = 2 is the classical AIC.

Details

The default method for AIC, AIC.default() entirely relies on the existence of a logLik method computing the log-likelihood for the given class.

When comparing fitted objects, the smaller the AIC, the better the fit.

Value

If just one object is provided, returns a numeric value with the corresponding AIC (or BIC, or ..., depending on k); if more than one object are provided, returns a data.frame with rows corresponding to the objects and columns representing the number of parameters in the model (df) and the AIC.

Author(s)

Jose Pinheiro and Douglas Bates

References

Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.

See Also

logLik, AIC.logLik.

Examples

data(swiss)
lm1 <- lm(Fertility ~ . , data = swiss)
AIC(lm1)
stopifnot(all.equal(AIC(lm1),
                    AIC(logLik(lm1))))
## a version of BIC or Schwarz' BC :
AIC(lm1, k = log(nrow(swiss)))

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