\HeaderA{stepAIC}{Choose a model by AIC in a Stepwise Algorithm}{stepAIC}
\aliasA{extractAIC.gls}{stepAIC}{extractAIC.gls}
\aliasA{extractAIC.lme}{stepAIC}{extractAIC.lme}
\aliasA{terms.gls}{stepAIC}{terms.gls}
\aliasA{terms.lme}{stepAIC}{terms.lme}
\keyword{models}{stepAIC}
\begin{Description}\relax
Performs stepwise model selection by exact AIC.
\end{Description}
\begin{Usage}
\begin{verbatim}
stepAIC(object, scope, scale = 0,
        direction = c("both", "backward", "forward"),
        trace = 1, keep = NULL, steps = 1000, use.start = FALSE,
        k = 2, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] an object representing a model of an appropriate class.
This is used as the initial model in the stepwise search.

\item[\code{scope}] defines the range of models examined in the stepwise search.
This should be either a single formula, or a list containing
components \code{upper} and \code{lower}, both formulae.  See the
details for how to specify the formulae and how they are used.

\item[\code{scale}] used in the definition of the AIC statistic for selecting the models,
currently only for \code{\LinkA{lm}{lm}} and \code{\LinkA{aov}{aov}} models
(see \code{\LinkA{extractAIC}{extractAIC}} for details).

\item[\code{direction}] the mode of stepwise search, can be one of \code{"both"},
\code{"backward"}, or \code{"forward"}, with a default of \code{"both"}.
If the \code{scope} argument is missing the default for
\code{direction} is \code{"backward"}.

\item[\code{trace}] if positive, information is printed during the running of
\code{stepAIC}.
Larger values may give more information on the fitting process.

\item[\code{keep}] a filter function whose input is a fitted model object and the
associated \code{AIC} statistic, and whose output is arbitrary.
Typically \code{keep} will select a subset of the components of
the object and return them. The default is not to keep anything.

\item[\code{steps}] the maximum number of steps to be considered.  The default is 1000
(essentially as many as required).  It is typically used to stop the
process early.

\item[\code{use.start}] if true the updated fits are done starting at the linear predictor for
the currently selected model. This may speed up the iterative
calculations for \code{glm} (and other fits), but it can also slow them
down. \bold{Not used} in \R.

\item[\code{k}] the multiple of the number of degrees of freedom used for the penalty.
Only \code{k = 2} gives the genuine AIC: \code{k = log(n)} is
sometimes referred to as BIC or SBC.

\item[\code{...}] any additional arguments to \code{extractAIC}. (None are currently used.)

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The set of models searched is determined by the \code{scope} argument.
The right-hand-side of its \code{lower} component is always included
in the model, and right-hand-side of the model is included in the
\code{upper} component.  If \code{scope} is a single formula, it
specifes the \code{upper} component, and the \code{lower} model is
empty.  If \code{scope} is missing, the initial model is used as the
\code{upper} model.

Models specified by \code{scope} can be templates to update
\code{object} as used by \code{\LinkA{update.formula}{update.formula}}.

There is a potential problem in using \code{\LinkA{glm}{glm}} fits with a
variable \code{scale}, as in that case the deviance is not simply
related to the maximized log-likelihood. The \code{glm} method for
\code{\LinkA{extractAIC}{extractAIC}} makes the
appropriate adjustment for a \code{gaussian} family, but may need to be
amended for other cases. (The \code{binomial} and \code{poisson}
families have fixed \code{scale} by default and do not correspond
to a particular maximum-likelihood problem for variable \code{scale}.)

Where a conventional deviance exists (e.g. for \code{lm}, \code{aov}
and \code{glm} fits) this is quoted in the analysis of variance table:
it is the \emph{unscaled} deviance.
\end{Details}
\begin{Value}
the stepwise-selected model is returned, with up to two additional
components.  There is an \code{"anova"} component corresponding to the
steps taken in the search, as well as a \code{"keep"} component if the
\code{keep=} argument was supplied in the call. The
\code{"Resid. Dev"} column of the analysis of deviance table refers
to a constant minus twice the maximized log likelihood: it will be a
deviance only in cases where a saturated model is well-defined
(thus excluding \code{lm}, \code{aov} and \code{survreg} fits,
for example).
\end{Value}
\begin{Note}\relax
The model fitting must apply the models to the same dataset.  This may
be a problem if there are missing values and an \code{na.action} other than
\code{na.fail} is used (as is the default in \R).
We suggest you remove the missing values first.
\end{Note}
\begin{References}\relax
Venables, W. N. and Ripley, B. D. (2002)
\emph{Modern Applied Statistics with S.} Fourth edition.  Springer.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{addterm}{addterm}}, \code{\LinkA{dropterm}{dropterm}}, \code{\LinkA{step}{step}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
quine.stp <- stepAIC(quine.nxt,
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1),
    trace = FALSE)
quine.stp$anova

cpus1 <- cpus
attach(cpus)
for(v in names(cpus)[2:7])
  cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])),
                    include.lowest = TRUE)
detach()
cpus0 <- cpus1[, 2:8]  # excludes names, authors' predictions
cpus.samp <- sample(1:209, 100)
cpus.lm <- lm(log10(perf) ~ ., data = cpus1[cpus.samp,2:8])
cpus.lm2 <- stepAIC(cpus.lm, trace = FALSE)
cpus.lm2$anova

example(birthwt)
birthwt.glm <- glm(low ~ ., family = binomial, data = bwt)
birthwt.step <- stepAIC(birthwt.glm, trace = FALSE)
birthwt.step$anova
birthwt.step2 <- stepAIC(birthwt.glm, ~ .^2 + I(scale(age)^2)
    + I(scale(lwt)^2), trace = FALSE)
birthwt.step2$anova

quine.nb <- glm.nb(Days ~ .^4, data = quine)
quine.nb2 <- stepAIC(quine.nb)
quine.nb2$anova
\end{ExampleCode}
\end{Examples}

