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I am currently researching silence in the social sciences and am reviewing surveys and statistical methods implemented by researchers to get an idea methods in both survey design and the analysis currently being used in the field.

I am a reading a paper where the authors perform a "A principal component factor analysis with oblimin rotation" where they identified nine factors with loadings. They used a scree test to determine the number of factors

This to me seems like they implemented an exploratory factor analysis, as a PCA - as far as my understanding goes - is a data reduction technique which produces uncorrelated principle components and not factors.

Based on the information above can someone confirm my understanding? It just isn't clear to me in the paper why they have called it a principal component factor analysis.

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    $\begingroup$ Unfortunately it is difficult to say without more context of that article what concretely the authors meant. Either they (1) used PCA as factor analysis or they(2) did Principal axis method Factor analysis. Or they (3) even might mean other things, such as probabilistic PCA; or categorical PCA which sometimes goes by nick "nonlinear FA". $\endgroup$ – ttnphns Jul 18 '15 at 6:24
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    $\begingroup$ Hi @ttnphns, to quote the full analysis they say - "A principal component factor analysis with oblimin rotation was carried out for study 1 in order to explore the factor structure of the measure. The factor analysis identified nine factors with eigenvalues above the cut-off point of 1.0 explaining 64 percent of the total variance. Subsequently, the scree test was used in order to decide upon the number of the main factors (Kline,1994), after which five main factors were identified" which based on your link looks like Principal Axis (= Principal Factor with iterations) $\endgroup$ – John Smith Jul 18 '15 at 6:32
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    $\begingroup$ Hmm, no clue yet, in the citation. I suspect that they may have used just PCA as well. $\endgroup$ – ttnphns Jul 18 '15 at 6:43
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    $\begingroup$ in issuu.com/inikol/docs/pr_final/17 (after searching for the phrase around the term "oblimin") it seems, that they have used pca for find the number of relevant factors, and have then applied the FA-procedure for this number of factors: "(...) subsequent FA requesting 5 factors (...)"(middle of the left side in the flash-animation of the text). <p> <\p>*(No warranty that I got things correctly)* $\endgroup$ – Gottfried Helms Jul 18 '15 at 8:56
  • $\begingroup$ I think this problem may have to do with stata. The have a -pca- (principal component analysis) option as well as a -factor varlist, pcf- (principal component factor). $\endgroup$ – hanne Nov 7 '16 at 19:58
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PCA is different to EFA. In PCA, we don't have a hypothesis of the underlying structure of the data. We use PCA to simplify the dimension of the data, for each eigenvector. In EFA, we have a number of latent constructs which we want to run the analysis. Apart from the overall goal, the analysis and calculation is very similar.

In the paper, I think the authors performed a PCA with a rotation for the factors to improve the interpretation of the components. To quote @ttnphns in his answer on PCA vs FA:

PCA: rotation/interpretation of components - sometimes

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Confusingly, "principal component" is the name of one method for estimating the parameters of a factor analysis model. See https://newonlinecourses.science.psu.edu/stat505/node/78/ for further details. This estimation method is available in at least SAS, Stata (as noted above, the pcf option to factor), and R (in the psych package, possibly others too). It is distinct from, although related to, a principal component analysis.

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