AIC {stats}

R Documentation

Akaike's An 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.

The log-likelihood and hence the AIC is only defined up to an additive constant. Different constants have conventionally be used for different purposes and so extractAIC and AIC may give different values (and do for models of class "lm": see the help for extractAIC).

Value

If just one object is provided, returns a numeric value with the corresponding AIC (or BIC, or ..., depending on k); if multiple objects 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

extractAIC, logLik.

Examples

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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