| % File src/library/stats/man/extractAIC.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2014 R Core Team |
| % Distributed under GPL 2 or later |
| |
| %-- This page by Martin Maechler, improvements welcome! |
| \name{extractAIC} |
| \title{Extract AIC from a Fitted Model} |
| % |
| \alias{extractAIC} |
| \usage{ |
| extractAIC(fit, scale, k = 2, \dots) |
| } |
| \arguments{ |
| \item{fit}{fitted model, usually the result of a fitter like |
| \code{\link{lm}}.} |
| \item{scale}{optional numeric specifying the scale parameter of the |
| model, see \code{scale} in \code{\link{step}}. Currently only used |
| in the \code{"lm"} method, where \code{scale} specifies the estimate |
| of the error variance, and \code{scale = 0} indicates that it is to |
| be estimated by maximum likelihood. |
| } |
| \item{k}{numeric specifying the \sQuote{weight} of the |
| \emph{equivalent degrees of freedom} (\eqn{\equiv}{=:} \code{edf}) |
| part in the AIC formula.} |
| \item{\dots}{further arguments (currently unused in base \R).} |
| } |
| %-- Source in ../R/add.R |
| \description{ |
| Computes the (generalized) Akaike \bold{A}n \bold{I}nformation |
| \bold{C}riterion for a fitted parametric model. |
| } |
| \details{ |
| This is a generic function, with methods in base \R for classes |
| \code{"aov"}, \code{"glm"} and \code{"lm"} as well as for |
| \code{"negbin"} (package \CRANpkg{MASS}) and \code{"coxph"} and |
| \code{"survreg"} (package \CRANpkg{survival}). |
| |
| The criterion used is |
| \deqn{AIC = - 2\log L + k \times \mbox{edf},}{AIC = - 2*log L + k * edf,} |
| where \eqn{L} is the likelihood and \code{edf} the equivalent degrees |
| of freedom (i.e., the number of free parameters for usual parametric |
| models) of \code{fit}. |
| |
| For linear models with unknown scale (i.e., for \code{\link{lm}} and |
| \code{\link{aov}}), \eqn{-2\log L}{-2 log L} is computed from the |
| \emph{deviance} and uses a different additive constant to |
| \code{\link{logLik}} and hence \code{\link{AIC}}. If \eqn{RSS} |
| denotes the (weighted) residual sum of squares then \code{extractAIC} |
| uses for \eqn{- 2\log L}{-2 log L} the formulae \eqn{RSS/s - n} (corresponding |
| to Mallows' \eqn{C_p}{Cp}) in the case of known scale \eqn{s} and |
| \eqn{n \log (RSS/n)}{n log (RSS/n)} for unknown scale. |
| \code{\link{AIC}} only handles unknown scale and uses the formula |
| \eqn{n \log (RSS/n) + n + n \log 2\pi - \sum \log w}{n*log(RSS/n) + n + n*log 2pi - sum(log w)} |
| where \eqn{w} are the weights. Further \code{AIC} counts the scale |
| estimation as a parameter in the \code{edf} and \code{extractAIC} does not. |
| |
| For \code{glm} fits the family's \code{aic()} function is used to |
| compute the AIC: see the note under \code{logLik} about the |
| assumptions this makes. |
| |
| \code{k = 2} corresponds to the traditional AIC, using \code{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 \code{\link{AIC}} (usually |
| \emph{via} a method for \code{\link{logLik}}). We have already |
| mentioned the case of \code{"lm"} models with estimated scale, and |
| there are similar issues in the \code{"glm"} and \code{"negbin"} |
| methods where the dispersion parameter may or may not be taken as |
| \sQuote{free}. This is immaterial as \code{extractAIC} is only used |
| to compare models of the same class (where only differences in AIC |
| values are considered). |
| } |
| \note{ |
| This function is used in \code{\link{add1}}, \code{\link{drop1}} |
| and \code{\link{step}} and the similar functions in package |
| \CRANpkg{MASS} from which it was adopted. |
| } |
| \value{ |
| A numeric vector of length 2, with first and second elements giving |
| |
| \item{edf}{the \sQuote{\bold{e}quivalent \bold{d}egrees of \bold{f}reedom} |
| for the fitted model \code{fit}.} |
| |
| \item{AIC}{the (generalized) Akaike Information Criterion for \code{fit}.} |
| } |
| %-- Source in ../R/add.R |
| \author{B. D. Ripley} |
| \references{ |
| Venables, W. N. and Ripley, B. D. (2002) |
| \emph{Modern Applied Statistics with S.} |
| New York: Springer (4th ed). |
| } |
| \seealso{ |
| \code{\link{AIC}}, \code{\link{deviance}}, \code{\link{add1}}, |
| \code{\link{step}} |
| } |
| \examples{\donttest{ |
| utils::example(glm) |
| extractAIC(glm.D93) #>> 5 15.129 |
| }} |
| \keyword{models} |