extractAIC {stats}R Documentation

Extract AIC from a Fitted Model


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).

See Also

AIC, deviance, add1, step


extractAIC(glm.D93)#>>  5  15.129

[Package stats version 2.5.0 Index]