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I have a table with the factor loadings obtained from a PCA for each variable and each component. Is it possible only with these data to obtain the eigenvalues for each Principal Component?

sbac
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  • For each component, eigenvalue (PC variance) is the sum of squared loadings. This is true when components were not rotated obliquely. Note terminologically loading is not the synonym of eigenvector entry (search this site PCA loadings eigenvectors) – ttnphns Jun 24 '17 at 15:40
  • But if they were rotated not obliquely the answer is the same? – sbac Jun 24 '17 at 15:44
  • yes orthogonal rotation supports what I wrote – ttnphns Jun 24 '17 at 15:54
  • Please transform your comment in answer for voting if you please. – sbac Jun 24 '17 at 15:57
  • Just to be clear: You mean by loadings you mean the PC scores, the projection of the original zero-centred dataset to the space spanned by the eigenvectors, right? – usεr11852 Jun 24 '17 at 19:21
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    @ttnphns If components were rotated orthogonally, then of course the variance is still given by the sum of squares, but I don't think one call it "eigenvalue" anymore. – amoeba Jun 24 '17 at 19:24
  • @amoeba: +1. Was playing with some MATLAB examples exactly for this... In addition I think that as we work with finite samples we would want something like $\frac{N+1}{N} \frac{1}{N} \sum_i^N \xi_j^2 $ instead of just a sum of squares... ie. the sample variance. ($\xi_j$ being the scores associated with the $j$-th PC, $N$ the number of items in the sample.) – usεr11852 Jun 24 '17 at 19:34
  • @usεr11852 Note: loadings are NOT scores. Usually, "loadings" are meant to be PCA eigenvectors multiplied by the square root of the respective eigevalue. – amoeba Jun 24 '17 at 19:43
  • @amoeba: Probably? Maybe? I asked the OP what is meant in this case. I find the term "loadings" so loaded... – usεr11852 Jun 24 '17 at 19:48
  • @amoeba, yes of course, thanks for making the pin. In this my comment yes orthogonal rotation... I actually meant just variance, not eigenvalues anymore. Both you and I would show that elsewhere. – ttnphns Jun 24 '17 at 19:54

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