| 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
|
... |
optionally more fitted model objects. |
k |
numeric, the penalty per parameter to be used; the
default |
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)))