extractAIC {stats}  R Documentation 
Computes the (generalized) Akaike An Information Criterion for a fitted parametric model.
extractAIC(fit, scale, k = 2, ...)
fit 
fitted model, usually the result of a fitter like
lm . 
scale 
optional numeric specifying the scale parameter of the
model, see scale in step . Currently only used
in the "lm" method, where scale specifies the estimate
of the error variance, and scale = 0 indicates that it is to
be estimated by maximum likelihood.

k 
numeric specifying the “weight” of the
equivalent degrees of freedom (=: edf )
part in the AIC formula. 
... 
further arguments (currently unused in base R). 
This is a generic function, with methods in base R for "aov"
,
"coxph"
, "glm"
, "lm"
, "negbin"
and "survreg"
classes.
The criterion used is
AIC =  2*log L + k * edf,
where L is the likelihood and edf
the equivalent degrees
of freedom (i.e., the number of free parameters for usual parametric
models) of fit
.
For linear models with unknown scale (i.e., for lm
and
aov
), 2log L is computed from the
deviance and uses a different additive constant to
logLik
and hence AIC
. If RSS
denotes the (weighted) residual sum of squares then extractAIC
uses for  2log L the formulae RSS/s  n (corresponding
to Mallows' Cp) in the case of known scale s and
n log (RSS/n) for unknown scale. AIC
only handles
unknown scale and uses the formula
n log (RSS/n)  n + n log 2π  sum log w
where w are the weights.
For glm
fits the family's aic()
function to compute the
AIC: see the note under logLik
about the assumptions this makes.
k = 2
corresponds to the traditional AIC, using k =
log(n)
provides the BIC (Bayesian IC) instead.
A numeric vector of length 2, giving
edf 
the “equivalent degrees of freedom”
for the fitted model fit . 
AIC 
the (generalized) Akaike Information Criterion for fit . 
This function is used in add1
, drop1
and step
and similar functions in package MASS
from which it was adopted.
B. D. Ripley
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer (4th ed).
example(glm) extractAIC(glm.D93)#>> 5 15.129