# What does “varimax” mean in factor analysis?

In the rotation options of SPSS Factor Analysis, there is a rotation method named "Varimax". If I choose this option, does it mean the orthogonal rotation technique of Principal Component Analysis will be applied on the factor loadings by analyzing the co-variance matrix of the factor loadings? (Because "varimax" sounds a bit like "maximizing variance", which is what PCA does.)

• Did you give a try to type "varimax" in Google search? – ttnphns Apr 6 '15 at 8:21
• The answer to your question is NO, despite what the accepted answer says. Varimax has no direct relationship to PCA. – amoeba says Reinstate Monica Sep 21 '17 at 22:38

I think that the answer to your question is Yes (at least, in the big picture sense). Should you be wanting to dive deeper into details, I would suggest you to review this excellent discussion here on Cross Validated, especially an answer by @amoeba and/or Chapter 6 of the excellent online book by Revelle (2015). Having said that, I would like to make the following points:

• Varimax and other rotation methods, are not specific to SPSS, as they are general exploratory factor analysis (EFA) terms (so maybe spss tag should be deleted from the question).

• While varimax is the most popular option across research literature (this is likely the reason it is the default option for psych::factanal() in R) and usually produces simpler, easier to interpret, factor solutions, since all orthogonal rotation methods produce uncorrelated factors, they often are not the best. Oblique transformation methods, due to allowing factors to correlate, produce less simple models, however, it is argued that it is beneficial, since such models more accurately reflect reality, in other words, have higher explanatory power, with an additional benefit of better reproducibility of the results (Costello & Osborne, 2005).

• I think that, following the tradition of the exploratory data analysis and research, it is much better to try several EFA approaches and methods and choose the optimal one, based not only on analytical fit indices, but first and foremost, based on making sense within the theory around studied constructs (if it exists) or domain knowledge (if developed theories don't yet exist for the domain under study).

References

Costello, A. B., & Osborne, J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10(7). Retrieved from http://pareonline.net/pdf/v10n7.pdf

Revelle, W. (2015). An introduction to psychometric theory with applications in R. [Website] Retrieved from http://www.personality-project.org/r/book

• +1. The only things I would add to this explanation are: 1) orthogonal v. oblique rotation does not produce factors that are uncorrelated or correlated, respectively. The two approaches simply differ with respect to what they assume; orthogonal methods assume variables are uncorrelated, so the correlation is not estimated. Oblique methods do not make this assumption and so correlations are estimated. And 2) oblique models are not necessarily less simple. In fact, when factors are truly correlated, oblique solutions possess greater simple structure (Fabrigar & Wegener, 2012) – jsakaluk Apr 6 '15 at 20:29
• @jsakaluk: Thank you for upvoting and your comment. I will keep your points in mind, when I will get a chance to update my answer. – Aleksandr Blekh Apr 6 '15 at 22:03
• @Tony: My pleasure! – Aleksandr Blekh Apr 7 '15 at 2:08
• I think that the answer to your question is Yes (at least, in the big picture sense). - This is wrong, the answer to this question is NO. Varimax factor rotation has nothing to do with PCA. The remaining part of your answer is okay, but this first sentence is plain wrong and quite misleading. – amoeba says Reinstate Monica Sep 21 '17 at 22:35
• @amoeba Thank you for your comment - it was quite a while ago to remember my exact line of thinking. :-) But, I guess, because of only indirect relation between of the two concepts I have used the phrase in the big picture sense. I agree that a direct answer to the question in NO (I likely wanted to emphasize some conceptual similarity - sorry, don't remember details). Please feel free to update my answer with your clarification. – Aleksandr Blekh Sep 22 '17 at 1:01