Please check it up:

https://stats.stackexchange.com/questions/50745/best-factor-extraction-methods-in-factor-analysis

In my opinion, PCA is the best, because it helps the analysis process to differentiate the elements successfully for determining the main factors.

Good Luck.

You have a hypothesized two-factor structure. I assume you are planning some form of CFA. Can you say something about the distribution of items and did you discover anything to note when examining the scatter plots?

Avoid Principal Components Analysis (PCA), because it seldom meets the assumptions of social science data. Beyond PCA, the other methods should give similar results.

For rotation, I always recommend correlated factors (oblique rotation) because it is seldom realistic to assume that your factors are unrelated to each other (orthogonal rotation).

Daniel Wright

I am planing CFA. Two factors are theoretically related to each other. One include the other. But I don't know if it's statistical. How can i understand?

Ali Can , this should be covered in most latent variable courses that you would take. I would not do these analyses prior to having sufficient training. David L Morgan , which assumptions are you referring to that PCA has problems with in reference to the social sciences? I always think of PCA as just a data reduction technique (the eigenvalues), but I guess if you planned to use the results in some other ways you'd be making assumptions.

I was taught that it is an issue of the assumptions about the commonalities in PCA versus Principal Factors Analysis, in terms of the kinds of things we want to measure in the social sciences. But that was a long time ago and the details escape me now.

Of course, now that so many people do SEM and CFA, I would say that Maximum Likelihood is the best choice, in order to match those approaches.

Maximum likelihood as it gives chance only which does not mislead

For an excellent guide for how to decide on the right approach see:

Hair JF, Black WC, Babin BJ, et al. (2014) Multivariate Data Analysis. 7th ed.: Pearson Education Limited.

Exploratory factor analysis (EFA) is used when theory development process such as initial development of a new research instrument and when researcher use EFA, researchers have little or no information about underlying factor structure of instrument/scale. Principal component analysis is a data reduction technique of ten used to reduce a large number of variables to smaller components.

In your case using Confirmatory factor analysis is more appropriate. Because underlying factor structure of the scale is known.

Maximum likelihood extraction is suggested when data are relatively normally distributed and when the intention of EFA is to obtain interpretable factors, rather than remove items. Oblique rotations allow factors to correlate and therefore they are more realistic for social sciences research. Orthogonal rotations do not allow factors to correlate and they may lead to loss of valuable data if used when factors being studied correlate.

I did transcultural validation of an instrument and made justifications to my choices based on well-reputed sources. Also, you may want to have a look at a RG discussion of whether you should go for EFA or CFA in transcultural adaptation. Please refer to the links below.

Article Psychometric Properties of an Arabic Version of the Patient ...

https://www.researchgate.net/post/In_validation_of_a_transculturally_adapted_scale_what_should_be_done_first_exploratory_factor_analysis_or_confirmatory_factor_analysis

Article Korean Patient-Perceived Satisfaction Scale of Community-Bas...

Oblique rotation is the right rotation method in social science. However, I performed a varimax rotation and then defended why I did in the article. The article will be of help to you.

My workflow is usually:

* no rotation

* orthogonal rotation (Varimax)

* oblique rotation (Promax, which is "relaxed" orthogonal)

If there is no significant difference - ok, no rotation

Orthogonal is much different - my variables are more "independent". Are they?

Promax is much different - there are 2 (spectral) components which are almost overlapped

But the key deciding factor is to be lucky and know that to expect to see as the components. If those have physical meaning - fine. Otherwise - don't use factor analysis at all!

Why? Because if the extracted (spectral) component is wrong - the "concentrations" are wrong as well!

On my blog, I covered 4 questions from RG. If you are new in PCA - it could be worth reading: https://www.steemstem.io/#!/@alexs1320/answering-4-rg-quest

I am an Assistant professor, have published four psychometric papers, and teach a PhD-level assessment course. I am confident in my response below. For a good summaries, see Worthington & Whittaker (2006) and Kahn (2006).

Short answer:

• Extraction: Principal Axis Factoring
• Rotation: Promax or Direct Oblimin

Long answer:

• Extraction: Use Principal Axis Factoring. PCA assumes no error. It uses all of the variance: error, common variance between items, and unique variance that the specific items do not share with the common factor and is not error. This is not consistent with social science, as error exists. PAF uses commonalities. ML is good if the data are multivariate normal, but researchers say that ML/PAF results are so similar that PAF is a good choice in any scenario. Again, DO NOT USE PCA.
• Also, once you've used PAF, make sure you use scree plot and parallel analysis to determine the number of factors--DO NOT rely on the Eigenvalue > 1 rule. You can overestimate the number of factors if you do (the papers I recommended explain this in greater detail). This is a common mistake.
• Rotation: There are different thoughts around this. Varimax assumes the factors are not correlated (orthogonal). Therefore, you will get factors that are very different BUT this is not consistent with social science. If you're creating a scale with multiple dimensions of a related construct, they will correlate. Therefore, researchers favor oblique rotations (specifically, direct oblimin) because they allow the factors to correlate. In addition, promax is also a great rotation and recommended because it is a nice compromise; Promax first assumes the factors are orthogonal and then relaxes the rotation to allow them to correlate (Russell, 2002). You can run both oblimin and promax and see if the results are different (as far as which items you keep; specific factor loadings will be a little different). You will likely retain the same items in both of those rotations; you could report that in your paper, which strengthens the results.

The following Chapter is an introduction to factor analysis (PCA, EFA and CFA), which has been cited in more than 1,500 published articles (Google Scholar). The book in which the chapter appears is available in more than 10,000 libraries world-wide, and should be available at or via your academic library. Unfortunately the copyright is owned by the publisher therefore I am NOT able to legally disseminate copies.

Bryant, F.B., & Yarnold, P.R. Principal components, and exploratory and confirmatory factor analysis. In: L.G. Grimm and P.R. Yarnold (Eds.), Reading and Understanding Multivariate Statistics. Washington, DC: APA Books, 1995, 99-136.

Hello Dear @Ali Can,

You can read Andy Field's SPSS Statistics book. But I think you have to use Confirmatory Factor Analysis (CFA) instead of Explatory Factor Analysis (EFA) for adaptation of scale.

Follow-up to my previous answer: My response applies to conducting an EFA. As Iskender mentioned, your situation uses an existing measure and thus requires a confirmatory factor analysis (CFA). You can't conduct a CFA in SPSS as far as I'm aware. SPSS does not allow you specify which items go onto which factor and the output does provide much relevant CFA information. Instead, you want want to use a structural model and report the fit indices (CFI, TLI, RMSEA, SRMR). This can be done in programs such as MPlus and LISREL.

SPSS supports an additional program called AMOS that does CFA, and there is a macro called PROCESS that is supposed to do CFA within SPSS -- I say "supposed to" because I am not personally familiar with it.

Principal axis factoring using the Promax rotation.

What should be the cut value to retain the loadings when objective is the data reduction?