The eigen function is for extracting components, not factor analysis.

Try to use SPSS software for factor analysis. It is more efficient than R.

Good Luck.

Five Variable and Five Component. This result indicates that Factor Analysis is not suitable for your study data. No matter what software you use.

Mosayeb Dashtpeyma , please say in what way you think the SPSS procedure is more efficient than some function in R. Does "more efficient" mean fewer iterations? I am not arguing for or against SPSS, but if you have some interesting evidence to support your statement I would be interested in it.

Daniel Wright , Please check it up:

https://www.educba.com/r-vs-spss/

Good Luck.

Mosayeb Dashtpeyma , you've pointed readers to a comparison between SPSS and R, which mentions pros and cons of each (and seems to compare base R with SPSS, but it isn't very clear), but is not about factor analysis and you don't answer my question. Please define what you mean by "efficiency" and provide evidence (e.g., some simulation study) why you feel so strongly for this that you wrote it in a response. Please do this with reference factor analysis (and I assume you are talking about the base function factanal, though since the questioner used eigen this is efficient in the sense of processing speed compared with many other R functions as it uses LAPACK, http://www.netlib.org/lapack ). I am assuming you are referring to something like the number of iterations or the processing time or something like that.

Hi - When you use eigenvalues as with your first example, you fit an unknown covariance matrix to the observed covariance matrix using a least square criterion (Frobenius norm). When you use the R-function "factanal" the fitting problem is the same but the criterion is now a maximum likelihood one (see : https://en.wikipedia.org/wiki/Confirmatory_factor_analysis#Statistical_model).

It is not surprising that with two different criteria you get two different solutions (be aware that the orientations of axes are random with the first method).

If your next step is to be a test, the second method will allow you to use a likelihood ratio test. To my knowledge there is no such general test for the first method.

Best regards.