\Header{biplot.princomp}{Biplot for Principal Components}
\keyword{multivariate}{biplot.princomp}
\keyword{hplot}{biplot.princomp}
\begin{Description}\relax
Produces a biplot (in the strict sense) from the output of
\code{\Link{princomp}}.\end{Description}
\begin{Usage}
\begin{verbatim}
biplot(x, choices = 1:2, scale = 1, pc.biplot = FALSE, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] an object of class \code{"princomp"}.
\item[\code{choices}] length 2 vector specifying the components to plot. Only the default
is a biplot in the strict sense.

\item[\code{scale}] The variables are scaled by \code{lambda \textasciicircum{} scale} and the
observations are scaled by \code{lambda \textasciicircum{} (1-scale)} where
\code{lambda} are the singular values as computed by
\code{\Link{princomp}}. Normally \code{0 <= scale <= 1}, and a warning 
will be issued if the specified \code{scale} is outside this range.

\item[\code{pc.biplot}] If true, use what Gabriel (1971) refers to as a "principal component
biplot", with \code{lambda = 1} and observations scaled up by sqrt(n) and
variables scaled down by sqrt(n).  Then inner products between
variables approximate covariances and distances between observations
approximate Mahalanobis distance.

\item[\code{...}] optional arguments to be passed to
\code{\Link{biplot.default}}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
This is a method for the generic function \code{biplot}.  There is
considerable confusion over the precise definitions: those of the
original paper, Gabriel (1971), are followed here.  Gabriel and
Odoroff (1990) use the same definitions, but their plots actually
correspond to \code{pc.biplot = TRUE}.\end{Details}
\begin{Section}{Side Effects}
a plot is produced on the current graphics device.\end{Section}
\begin{References}\relax
Gabriel, K. R. (1971).
The biplot graphical display of matrices with applications to
principal component analysis.
\emph{Biometrika}, \bold{58}, 453--467.

Gabriel, K. R. and Odoroff, C. L. (1990).
Biplots in biomedical research.
\emph{Statistics in Medicine}, \bold{9}, 469--485.\end{References}
\begin{SeeAlso}\relax
\code{\Link{biplot}},
\code{\Link{princomp}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
data(USArrests)
biplot(princomp(USArrests))
\end{ExampleCode}
\end{Examples}

