| extractAIC {stats} | R Documentation |
Extract AIC from a Fitted Model
Description
Computes the (generalized) Akaike An Information Criterion for a fitted parametric model.
Usage
extractAIC(fit, scale, k = 2, ...)
Arguments
fit |
fitted model, usually the result of a fitter like
|
scale |
optional numeric specifying the scale parameter of the
model, see |
k |
numeric specifying the ‘weight’ of the
equivalent degrees of freedom ( |
... |
further arguments (currently unused in base R). |
Details
This is a generic function, with methods in base R for classes
"aov", "glm" and "lm" as well as for
"negbin" (package MASS) and "coxph" and
"survreg" (package survival).
The criterion used is
AIC = - 2\log L + k \times \mbox{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), -2\log 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 - 2\log L the formulae RSS/s - n (corresponding
to Mallows' C_p) 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 2\pi - \sum \log w
where w are the weights. Further AIC counts the scale
estimation as a parameter in the edf and extractAIC does not.
For glm fits the family's aic() function is used 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.
Note that the methods for this function may differ in their
assumptions from those of methods for AIC (usually
via a method for logLik). We have already
mentioned the case of "lm" models with estimated scale, and
there are similar issues in the "glm" and "negbin"
methods where the dispersion parameter may or may not be taken as
‘free’. This is immaterial as extractAIC is only used
to compare models of the same class (where only differences in AIC
values are considered).
Value
A numeric vector of length 2, with first and second elements giving
edf |
the ‘equivalent degrees of freedom’
for the fitted model |
AIC |
the (generalized) Akaike Information Criterion for |
Note
This function is used in add1, drop1
and step and the similar functions in package
MASS from which it was adopted.
Author(s)
B. D. Ripley
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer (4th ed).
See Also
Examples
utils::example(glm)
extractAIC(glm.D93) #>> 5 15.129