| 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