Could someone please explain the difference between the pca (principle component analysis) and pcf (principle component factoring) procedures in Stata? They both assume that there is no error/unique variance in each of the items (communalities = 1). Also, my understanding is that, in the unrotated solutions, they both produce orthogonal components/factors, which are usually presented in descending order of the variance of items accounted for.
Note that the usual explanation of the difference between principle component analysis and factor analysis models does not apply here (ie that the factor analysis model contains error/unique variance for each item, whereas principle component analysis does not), since in the pcf factor analysis procedure the communalities of the items are all set to one, so there is no error/uniqueness estimates, as in all other forms of factor analysis.
You may want to consider the commonalities of those items set to 1 and the initial rotation and you are to run the commonalities to see which items rotate well then you extract.
Extracting them will take you the the proper PCA where you can get the numbers of factors available through the eigenvalues. This is the PCA while the former is the procedure, which involves some analyses to be done.
Best of luck!!
Perhaps the Methods & Formulas sections of the documentation for the pca and factor commands will be helpful. (For the benefit of folks who do not use Stata, pca is a command, whereas pcf is an option for the factor command.)
- https://www.stata.com/manuals/mvpca.pdf
- https://www.stata.com/manuals/mvfactor.pdf
Alternatively, you could post your question to Statalist (which is followed by some StataCorp employees and many independent Stata users).
- https://www.statalist.org/forums/forum/general-stata-discussion/general
HTH.
John D Crawford, both pca and factor...,pcf are based on the same algorithm. pca displays eigenvectors whereas factor...,pcf shows factor loadings directly. However, if you type in estat loadings, cnorm(eigen) right after pca estimation, you will get the exact same factor loadings shown by factor...,pcf.
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