title: "Manual" Factor Analysis in R
body: <p>I am trying to follow along the Factor Analysis chapter in "Using Multivariate Statistics", by Tabachnick and Fidell.</p>
  
  <p>The data, and my steps, are as follows:</p>
  
  <pre><code># data
  dat.ski &lt;- data.frame(skiers = paste0("S", c(1:5), sep=""), cost = c(32, 61, 59, 36, 62), lift=c(64, 37, 40, 62, 46) , depth = c(65, 62, 45, 34, 43), powder = c(67, 65, 43, 35, 40))
  
  # correlation matrix
  cor.ski &lt;- cor(dplyr::select(dat.ski, -skiers)) 
  
  # eigenvalues and eigenvectors
  eig.ski &lt;- eigen(cor.ski)
  </code></pre>
  
  <p>The correlation matrix and eigenvalues (2.02, 1.94, 0.04 and 0.00) correspond to that in the book. The first two eigenvectors I have are (.352, -0.251, -0.626, -0.647) and (.514, -.664, .322, .280).   </p>
  
  <p>However, the book then continues to say that only the first two eigenvalues are retained and the "factor analysis is re-run" which results in the following two eigenvalues*: 2.00, 1.91 and eigenvectors (-2,83, 0.177, 0.568, 0.675) and (0.651, -0.685, 0.252, 0.207).  I can't work out to reproduce these eigenvectors... if I run <code>psych::fa(cor.ski, nfactors=2, fm="pa")</code>, the SS loadings correspond to the new eigenvalues*.</p>
  
  <p>Any help on how to return the eigenvectors as per the text will be greatly appreciated.</p>
  
  <p>Thanks.</p>