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% File src/library/stats/man/AIC.Rd
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% File src/library/stats/man/AIC.Rd
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% Part of the R package, http://www.R-project.org
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% Part of the R package, http://www.R-project.org
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% Copyright 1995-2012 R Core Team
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% Copyright 1995-2013 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{AIC}
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\name{AIC}
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\encoding{UTF-8}
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\encoding{UTF-8}
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\alias{AIC}
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\alias{AIC}
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  \item{\dots}{optionally more fitted model objects.}
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  \item{\dots}{optionally more fitted model objects.}
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  \item{k}{numeric, the \emph{penalty} per parameter to be used; the
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  \item{k}{numeric, the \emph{penalty} per parameter to be used; the
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    default \code{k = 2} is the classical AIC.}
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    default \code{k = 2} is the classical AIC.}
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}
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}
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\details{
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\details{
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  When comparing models fitted by maximum likelihood to the same data,
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  the smaller the AIC or BIC, the better the fit.
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  The theory of AIC requires that the log-likelihood has been maximized:
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  whereas AIC can be computed for models not fitted by maximum
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  likelihood, their AIC values should not be compared.
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  Examples of models not \sQuote{fitted to the same data} are where the
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  response is transformed (accelerated-life models are fitted to
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  log-times) and where contingency tables have been used to summarize
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  data.
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  These are generic functions (with S4 generics defined in package
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  These are generic functions (with S4 generics defined in package
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  \pkg{stats4}): however methods should be defined for the
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  \pkg{stats4}): however methods should be defined for the
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  log-likelihood function \code{\link{logLik}} rather than these
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  log-likelihood function \code{\link{logLik}} rather than these
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  functions: the action of their default methods is to call \code{logLik}
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  functions: the action of their default methods is to call \code{logLik}
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  on all the supplied objects and assemble the results.
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  on all the supplied objects and assemble the results.  Note that in
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  When comparing fitted objects, the smaller the AIC or BIC, the better
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  several common cases \code{\link{logLik}} does not return the value at
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  the fit.
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  the MLE: see its help page.
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  The log-likelihood and hence the AIC/BIC is only defined up to an
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  The log-likelihood and hence the AIC/BIC is only defined up to an
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  additive constant.  Different constants have conventionally be used
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  additive constant.  Different constants have conventionally been used
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  for different purposes and so \code{\link{extractAIC}} and \code{AIC}
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  for different purposes and so \code{\link{extractAIC}} and \code{AIC}
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  may give different values (and do for models of class \code{"lm"}: see
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  may give different values (and do for models of class \code{"lm"}: see
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  the help for \code{\link{extractAIC}}).  Particular care is needed
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  the help for \code{\link{extractAIC}}).  Particular care is needed
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  when comparing fits of different classes (with, for example, a
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  when comparing fits of different classes (with, for example, a
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  comparison of a Poisson and gamma GLM being meaningless since one has
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  comparison of a Poisson and gamma GLM being meaningless since one has