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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Biplot for Principal Components</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for biplot.princomp {stats}"><tr><td>biplot.princomp {stats}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2> Biplot for Principal Components </h2> <h3>Description</h3> <p>Produces a biplot (in the strict sense) from the output of <code><a href="princomp.html">princomp</a></code> or <code><a href="prcomp.html">prcomp</a></code> </p> <h3>Usage</h3> <pre> ## S3 method for class 'prcomp' biplot(x, choices = 1:2, scale = 1, pc.biplot = FALSE, ...) ## S3 method for class 'princomp' biplot(x, choices = 1:2, scale = 1, pc.biplot = FALSE, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>an object of class <code>"princomp"</code>.</p> </td></tr> <tr valign="top"><td><code>choices</code></td> <td> <p>length 2 vector specifying the components to plot. Only the default is a biplot in the strict sense. </p> </td></tr> <tr valign="top"><td><code>scale</code></td> <td> <p>The variables are scaled by <code>lambda ^ scale</code> and the observations are scaled by <code>lambda ^ (1-scale)</code> where <code>lambda</code> are the singular values as computed by <code><a href="princomp.html">princomp</a></code>. Normally <code>0 <= scale <= 1</code>, and a warning will be issued if the specified <code>scale</code> is outside this range. </p> </td></tr> <tr valign="top"><td><code>pc.biplot</code></td> <td> <p>If true, use what Gabriel (1971) refers to as a "principal component biplot", with <code>lambda = 1</code> 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. </p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>optional arguments to be passed to <code><a href="biplot.html">biplot.default</a></code>.</p> </td></tr> </table> <h3>Details</h3> <p>This is a method for the generic function <code>biplot</code>. 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</code>. </p> <h3>Side Effects</h3> <p>a plot is produced on the current graphics device. </p> <h3>References</h3> <p>Gabriel, K. R. (1971). The biplot graphical display of matrices with applications to principal component analysis. <em>Biometrika</em>, <b>58</b>, 453–467. doi: <a href="https://doi.org/10.2307/2334381">10.2307/2334381</a>. </p> <p>Gabriel, K. R. and Odoroff, C. L. (1990). Biplots in biomedical research. <em>Statistics in Medicine</em>, <b>9</b>, 469–485. doi: <a href="https://doi.org/10.1002/sim.4780090502">10.1002/sim.4780090502</a>. </p> <h3>See Also</h3> <p><code><a href="biplot.html">biplot</a></code>, <code><a href="princomp.html">princomp</a></code>. </p> <h3>Examples</h3> <pre> require(graphics) biplot(princomp(USArrests)) </pre> <hr /><div style="text-align: center;">[Package <em>stats</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>