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I'm doing an EFA on a scale that was designed to quantify LSD's effects. However we have a applied it in patients receiving Ketamine. We are doing the EFA because we wan't to see which items of the scale are relevant when applied for this purpose.

What I'm trying to understand is that when I run the EFA in SPSS, the first factor (Which contains only 3 items) has an Eigenvalue of 6.898, accounting for 29.9% variance. The next factor which contains most of the items has an Eigenvalue of 1.902, explaining 8.269% of variance.

BUT in the Extraction Sums of Squared Loadings, the first factor explains on 9.437% of variance and the second 24.015% of variance. What is the difference between these two measures? I've seen cases where they are slightly different, but here the second factor accounts for much more variance in the sums of squared analysis. Does this mean that this factor is indeed the one which accounts for more variance, despite initially having a much lower Eigenvalue?

Gerrit
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  • (My suspicion is that this is clear enough to someone who is expert in this area. I'm inclined to vote to leave open. It would be nice to hear from someone who knows factor analysis well.) – gung - Reinstate Monica Feb 09 '17 at 20:19
  • This question is a duplicate, it asks about issues explained in the link above. – ttnphns Feb 10 '17 at 03:48

2 Answers2

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The (unrotated) eigenvalues in factor analysis do not explain portions of total variance, they explain portions of common variance (i.e. variance not unique to each variable). These SPSS labels "Extraction Sums of Squared Loadings." The "Eigenvalues" in the first column result from an eigendecomposition of the correlation matrix: so these are eigenvalues from a PCA. The former will always be smaller than the latter.

Alexis
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    The 1st sentence is imprecise. Eigenvalues output in SPSS table are for PCA, therefore they are of total variance. Variances of factors are called "SS loadings" and they, too, are displayed - in % column - as % of total variance. Though these SS pertain to common portion of the variance only. – ttnphns Feb 10 '17 at 03:32
  • @ttnphns Thank you! Does the addition parenthetical second word) address your concern? – Alexis Feb 13 '17 at 19:44
  • Alexis, not quite. In _factor analysis_, we don't (normally) speak of "eigenvalues" of the extracted factors altogether. We speak of eigenvalues - as the variances of the components - in PCA. This is what was my answer (to where the link directs) about, you might want to read it. – ttnphns Feb 14 '17 at 09:32
  • @ttnphns Well, whether or not *you* speak of them all the Factor Analysis textbooks I have read (e.g., Gorsuch), *do* speak of eigenvalues, as do the software implementations of factor analysis in, say R, Stata, etc. Wait, which link? I don't see one in your comment. – Alexis Feb 14 '17 at 23:45
  • Alexis, I mean the link which is the thread the OP's question is recognized a duplicate of. Please read that thread attentively. In respect to your last claim - please give a reference (with context) when they `speak of eigenvalues`, so that I could read, to check how much the claim is correct. – ttnphns Feb 15 '17 at 04:21
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In the following link, search for f. Extraction Sums of Squared Loadings

As you can see in the table above it, the "Extraction" is merely copying over of the major contributory factors such that

f. Extraction Sums of Squared Loadings - The number of rows in this panel of the table correspond to the number of factors retained. In this example, we requested that three factors be retained, so there are three rows, one for each retained factor. The values in this panel of the table are calculated in the same way as the values in the left panel, except that here the values are based on the common variance. The values in this panel of the table will always be lower than the values in the left panel of the table, because they are based on the common variance, which is always smaller than the total variance.

The next part of the table refers to rotation of coordinates, which coordinates solve for independent conditions of transformed components. Described thus,

g. Rotation Sums of Squared Loadings - The values in this panel of the table represent the distribution of the variance after the varimax rotation. Varimax rotation tries to maximize the variance of each of the factors, so the total amount of variance accounted for is redistributed over the three extracted factors.

This changes the relative contribution of each component to the total variance, and may be where the confusion lies.

Now can you reproduce the corresponding table you have, please, so that we can see what information you are referring to.

Carl
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  • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - [From Review](/review/low-quality-posts/133918) – Juho Kokkala Feb 10 '17 at 06:41
  • @JuhoKokkala I would have had I not been afraid of violating copyright. It is an image not text, even though the SPSS original would have been formatted text. If you think it is not a violation of copyright, then I will copy. So, let me know, and trust me, it was not laziness. – Carl Feb 10 '17 at 07:02
  • Sorry, I don't know whether you can copy the image (I wouldn't). – Juho Kokkala Feb 10 '17 at 07:21
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    In any case the linked page is about principal component analysis, not factor analysis. See http://www.ats.ucla.edu/stat/spss/output/factor1.htm. – Scortchi - Reinstate Monica Feb 10 '17 at 11:17
  • @Scortchi Yeah, I'll buy that, and changed ans to reflect it. – Carl Feb 10 '17 at 17:52