I recently learned PCA and have the following questions on the use of principal() function of psych package:
From 20 variables I decided to keep 4 components / factors.
I used principal() function with rotation="oblimin". Since the factors could be related, I wanted to see the correlations between factors. So should I use r.scores or Phi on my pc object? What's the difference between them? At least on my current pc object they both give the same output. I don't see the principal() function's documentation mentions about r.scores.
When I don't extract any components, i.e., I specify nfactors = number of variables, and perform varimax roation and oblimin rotation I naturally get different factor loadings. a) In both case, the sum of eigenvalues (SS loadings) is equal to the number of variables. What's the reason for having sum of eigenvalues equal to the number of variables? b) For oblimin rotation, all 20 loadings for each factor as well as each variable are all zeros except one loading each which is 1. Basically each variable loads only on one factor. What's the rationale behind this?
When I use the oblimin rotation and then print the pc object, the factor loading matrix is the pattern matrix. How can I get or compute the structure matrix? I read that I should compare these two matrices if I have used an oblique rotation method. What should I look for in these matrices?