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AIC {stats}

Akaike's An Information Criterion
Package: 
stats
Version: 
R 2.15.3

Description

Generic function calculating Akaike's ‘An Information Criterion’ for one or several fitted model objects for which a log-likelihood value can be obtained, according to the formula -2*log-likelihood + k*npar, where npar represents the number of parameters in the fitted model, and k = 2 for the usual AIC, or k = log(n) (n being the number of observations) for the so-called BIC or SBC (Schwarz's Bayesian criterion).

Usage

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

BIC(object, ...)

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

These are generic functions (with S4 generics defined in package stats4): however methods should be defined for the log-likelihood function logLik rather than these functions: the action of their default methods is to call logLik on all the supplied objects and assemble the results. When comparing fitted objects, the smaller the AIC or BIC, the better the fit.

The log-likelihood and hence the AIC/BIC 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). Particular care is needed when comparing fits of different classes (with, for example, a comparison of a Poisson and gamma GLM being meaningless since one has a discrete response, the other continuous). BIC is defined as AIC(object, ..., k = log(nobs(object))). This needs the number of observations to be known: the default method looks first for a "nobs" attribute on the return value from the logLik method, then tries the nobs generic, and if neither succeed returns BIC as NA.

Values

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

If multiple objects are provided, a data.frame with rows corresponding to the objects and columns representing the number of parameters in the model (df) and the AIC or BIC.

References

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

See Also

extractAIC, logLik, nobs.

Examples

lm1 <- lm(Fertility ~ . , data = swiss)
AIC(lm1)
stopifnot(all.equal(AIC(lm1),
                    AIC(logLik(lm1))))
BIC(lm1)
 
lm2 <- update(lm1, . ~ . -Examination)
AIC(lm1, lm2)
BIC(lm1, lm2)

Author(s)

Originally by JoseTEXT Pinheiro and Douglas Bates, more recent revisions by R-core.

Documentation reproduced from R 2.15.3. License: GPL-2.