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% File src/library/stats/man/biplot.princomp.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{biplot.princomp}
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\alias{biplot.princomp}
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\alias{biplot.prcomp}
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\title{
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Biplot for Principal Components
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}
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\description{
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  Produces a biplot (in the strict sense) from the output of
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  \code{\link{princomp}} or \code{\link{prcomp}}
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}
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\usage{
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\method{biplot}{prcomp}(x, choices = 1:2, scale = 1, pc.biplot = FALSE, \dots)
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\method{biplot}{princomp}(x, choices = 1:2, scale = 1, pc.biplot = FALSE, \dots)
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}
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\arguments{
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  \item{x}{an object of class \code{"princomp"}.}
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  \item{choices}{
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    length 2 vector specifying the components to plot. Only the default
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    is a biplot in the strict sense.
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  }
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  \item{scale}{
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    The variables are scaled by \code{lambda ^ scale} and the
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    observations are scaled by \code{lambda ^ (1-scale)} where
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    \code{lambda} are the singular values as computed by
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    \code{\link{princomp}}.
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    Normally \eqn{0 \le \code{scale} \le 1}, and a warning
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    will be issued if the specified \code{scale} is outside this range.
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  }
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  \item{pc.biplot}{
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    If true, use what \bibcitet{R:Gabriel:1971} refers to as a
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    \dQuote{principal component biplot},
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    with \code{lambda = 1} and observations scaled up by sqrt(n) and
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    variables scaled down by sqrt(n).  Then inner products between
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    variables approximate covariances and distances between observations
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    approximate Mahalanobis distance.
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  }
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  \item{\dots}{optional arguments to be passed to
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    \code{\link{biplot.default}}.}
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}
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\section{Side Effects}{
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  a plot is produced on the current graphics device.
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}
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\details{
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  This is a method for the generic function \code{biplot}.  There is
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  considerable confusion over the precise definitions: those of the
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  original paper, \bibcitet{R:Gabriel:1971}, are followed here.
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  \bibcitet{R:Gabriel+Odoroff:1990} use the same definitions, but their
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  plots actually correspond to \code{pc.biplot = TRUE}.
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}
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\references{
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  \bibshow{*}
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}
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\seealso{
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    \code{\link{biplot}},
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    \code{\link{princomp}}.
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}
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\examples{
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require(graphics)
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biplot(princomp(USArrests))
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}
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\keyword{multivariate}
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\keyword{hplot}