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I conducted a principal component analysis (PCA) with direct oblimin factor rotation in SPSS.

Because by that time I didn't know any better, I used the COMPONENT MATRIX for interpretation. I added the items that loaded highest on factor one to form a scale, than I added the items that loaded highest on factor 2 and formed a scale of these items... After that, I tested for internal consistency with Cronbach's alpha and tested for correlations between sociodemographic data and my scales.

Now I found out that normally you interpret pattern or structure matrix. Interestingly both of them were NOT computed, only an error saying: Rotation failed to converge in 25 iterations. (Convergence = ,000).

Was my approach wrong? Is there something defendable about it or do I have to discard everything build on my (maybe wrong) assumption?

amoeba
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Mr. Threepwood
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  • "Rotation failed to converge in 25 iterations" - what rotation? – amoeba Oct 11 '16 at 16:26
  • Direct oblimin. – Mr. Threepwood Oct 11 '16 at 16:55
  • What if you increase the number of rotations, to say, 1000 ? – Gottfried Helms Oct 11 '16 at 17:22
  • When I enter 1000, the rotation converges in 30 iterations. – Mr. Threepwood Oct 11 '16 at 18:34
  • Thing is, I based selection of survey items to form components for one RQ of my master thesis on a grand part on my interpretation of the COMPONENT MATRIX and not of PATTERN or STRUCTURE MATRIX. My question was: Was my approach wrong? Is there something defendable about it or do I have to discard everything build on my (maybe wrong) assumption? – Mr. Threepwood Oct 12 '16 at 05:35
  • Any comments on my questions? – Mr. Threepwood Oct 12 '16 at 19:37
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    http://stats.stackexchange.com/q/166799/3277 – ttnphns Oct 13 '16 at 23:43
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    In the answers posted in the presented link, I couldn't find anything about the component matrix (thats a specific matrix outputted by spss next to the pattern and structure matrix) and their potential interpretation. – Mr. Threepwood Oct 14 '16 at 16:08
  • You should ping @ttnphns (by writing `@ttnphns`) if you want him to receive your replying comment. I did it for you now. – amoeba Oct 14 '16 at 16:09
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    @Mr.Threepwood, By "component" or "factor" matrix SPSS mean a matrix of loadings prior a rotation of factors (or components). So, you are asking if it is reasonable to interpret factors/compnents unrotated, right? One thread on this is [here](http://stats.stackexchange.com/q/82759/3277), and actually the link to it is present under the link "Q/A" in the first sentence of my answer http://stats.stackexchange.com/a/166823/3277 – ttnphns Oct 14 '16 at 19:34
  • @ttnphns! Yes, thats what I want to know! If I understand it right, rotation is done to find a potential simpler structure, but it is ok to not conduct rotation if you are more interested in the extracted component than in the potential underlying simpler structure? – Mr. Threepwood Oct 15 '16 at 07:19
  • @ttnphns: I conducted pca; I decided not to follow the > 1 Eigenvalue rule as that would have yielded too much components. So I had a look at the scree plot. The "bend" was at 2 and 4 components. I conducted pca from 1- 5 components solutions. The one with three made the most sense. So I retained those variables that loaded highest as indicated by the component matrix. Afterwards I tested for internal consistency (cronbach's alpha) and threw those out that dropped the value. The results make sense. Does my procedure too? – Mr. Threepwood Oct 17 '16 at 07:03
  • @amoeba Maybe you got a comment on my last question? ttnphns comments provided insights, how I can reward contributions that led to insights? – Mr. Threepwood Oct 19 '16 at 07:46
  • Sorry I don't know much about that. But if you only analyze "component matrix", this means you are not doing any "rotations", so you can simplify your presentation (currently you seem to be doing oblimin rotation but ignoring its outcome). – amoeba Oct 19 '16 at 15:46
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    @amoeba The oblimin rotation was not outputted in my case, because it failed to converge (see first poste). So if I understand the answers posted by ttnphns right, I interpreted an unrotated PCA while analyzing the component matrix. – Mr. Threepwood Nov 07 '16 at 10:22

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I would look at the component matrix for any variables that load in one component .500 or higher. Eliminate the others from your analysis variables and try again. Basically, some of the variables aren't loading strongly into any of the components and SPSS is trying to find a way to make them fit. Remove them, and you should be good to go.

sam
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