\HeaderA{boxcox}{Box-Cox Transformations for Linear Models}{boxcox}
\methaliasA{boxcox.default}{boxcox}{boxcox.default}
\methaliasA{boxcox.formula}{boxcox}{boxcox.formula}
\methaliasA{boxcox.lm}{boxcox}{boxcox.lm}
\keyword{regression}{boxcox}
\keyword{models}{boxcox}
\keyword{hplot}{boxcox}
\begin{Description}\relax
Computes and optionally plots profile log-likelihoods for the
parameter of the Box-Cox power transformation.
\end{Description}
\begin{Usage}
\begin{verbatim}
boxcox(object, ...)

## Default S3 method:
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'formula':
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'lm':
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] a formula or fitted model object.  Currently only \code{lm} and
\code{aov} objects are handled.
\item[\code{lambda}] vector of values of \code{lambda}
-- default \eqn{(-2, 2)}{} in steps of 0.1.
\item[\code{plotit}] logical which controls whether the result should be plotted.
\item[\code{interp}] logical which controls whether spline interpolation is
used. Default to \code{TRUE} if plotting with \code{lambda} of
length less than 100.
\item[\code{eps}] Tolerance for \code{lambda = 0}; defaults to 0.02.
\item[\code{xlab}] defaults to \code{"lambda"}.
\item[\code{ylab}] defaults to \code{"log-Likelihood"}.
\item[\code{...}] additional parameters to be used in the model fitting.
\end{ldescription}
\end{Arguments}
\begin{Value}
A list of the \code{lambda} vector and the computed profile
log-likelihood vector, invisibly if the result is plotted.
\end{Value}
\begin{Section}{Side Effects}
If \code{plotit = TRUE} plots loglik \emph{vs} \code{lambda} and
indicates a 95\% confidence interval about the maximum observed value
of \code{lambda}. If \code{interp = TRUE}, spline interpolation is
used to give a smoother plot.
\end{Section}
\begin{References}\relax
Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations (with discussion).
\emph{Journal of the Royal Statistical Society B}, \bold{26}, 211--252.

Venables, W. N. and Ripley, B. D. (2002)
\emph{Modern Applied Statistics with S.} Fourth edition.  Springer.
\end{References}
\begin{Examples}
\begin{ExampleCode}
data(trees)
boxcox(Volume ~ log(Height) + log(Girth), data = trees,
       lambda = seq(-0.25, 0.25, length = 10))

boxcox(Days+1 ~ Eth*Sex*Age*Lrn, data = quine,
       lambda = seq(-0.05, 0.45, len = 20))
\end{ExampleCode}
\end{Examples}

