# What is a "principal component factor analysis"?

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.

• 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". Commented Jul 18, 2015 at 6:24
• 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) Commented Jul 18, 2015 at 6:32
• Hmm, no clue yet, in the citation. I suspect that they may have used just PCA as well. Commented Jul 18, 2015 at 6:43
• 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)* Commented Jul 18, 2015 at 8:56
• 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). Commented Nov 7, 2016 at 19:58