| AIC {stats} | R Documentation |
Generic function calculating Akaike's 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).
AIC(object, ..., k = 2) BIC(object, ...)
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 |
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.
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.
Originally by José Pinheiro and Douglas Bates, more recent revisions by R-core.
Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.
extractAIC, logLik, nobs.
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)