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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: Rotation Methods for Factor Analysis</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 varimax {stats}"><tr><td>varimax {stats}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Rotation Methods for Factor Analysis</h2> <h3>Description</h3> <p>These functions ‘rotate’ loading matrices in factor analysis. </p> <h3>Usage</h3> <pre> varimax(x, normalize = TRUE, eps = 1e-5) promax(x, m = 4) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>A loadings matrix, with <i>p</i> rows and <i>k < p</i> columns</p> </td></tr> <tr valign="top"><td><code>m</code></td> <td> <p>The power used the target for <code>promax</code>. Values of 2 to 4 are recommended.</p> </td></tr> <tr valign="top"><td><code>normalize</code></td> <td> <p>logical. Should Kaiser normalization be performed? If so the rows of <code>x</code> are re-scaled to unit length before rotation, and scaled back afterwards.</p> </td></tr> <tr valign="top"><td><code>eps</code></td> <td> <p>The tolerance for stopping: the relative change in the sum of singular values.</p> </td></tr> </table> <h3>Details</h3> <p>These seek a ‘rotation’ of the factors <code>x %*% T</code> that aims to clarify the structure of the loadings matrix. The matrix <code>T</code> is a rotation (possibly with reflection) for <code>varimax</code>, but a general linear transformation for <code>promax</code>, with the variance of the factors being preserved. </p> <h3>Value</h3> <p>A list with components </p> <table summary="R valueblock"> <tr valign="top"><td><code>loadings</code></td> <td> <p>The ‘rotated’ loadings matrix, <code>x %*% rotmat</code>, of class <code>"loadings"</code>.</p> </td></tr> <tr valign="top"><td><code>rotmat</code></td> <td> <p>The ‘rotation’ matrix.</p> </td></tr> </table> <h3>References</h3> <p>Hendrickson, A. E. and White, P. O. (1964). Promax: a quick method for rotation to orthogonal oblique structure. <em>British Journal of Statistical Psychology</em>, <b>17</b>, 65–70. doi: <a href="https://doi.org/10.1111/j.2044-8317.1964.tb00244.x">10.1111/j.2044-8317.1964.tb00244.x</a>. </p> <p>Horst, P. (1965). <em>Factor Analysis of Data Matrices</em>. Holt, Rinehart and Winston. Chapter 10. </p> <p>Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. <em>Psychometrika</em>, <b>23</b>, 187–200. doi: <a href="https://doi.org/10.1007/BF02289233">10.1007/BF02289233</a>. </p> <p>Lawley, D. N. and Maxwell, A. E. (1971). <em>Factor Analysis as a Statistical Method</em>, second edition. Butterworths. </p> <h3>See Also</h3> <p><code><a href="factanal.html">factanal</a></code>, <code><a href="../../datasets/html/Harman74.cor.html">Harman74.cor</a></code>.</p> <h3>Examples</h3> <pre> ## varimax with normalize = TRUE is the default fa <- factanal( ~., 2, data = swiss) varimax(loadings(fa), normalize = FALSE) promax(loadings(fa)) </pre> <hr /><div style="text-align: center;">[Package <em>stats</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>