How can I test whether the oblimin exploratory factor analysis function in r has produced the most simple structure?

Question

would anyone know what command could be used to test whether the oblimin exploratory factor analysis function in r has produced the most simple structure? (as my understanding is oblimin does not always produce the most simple structure and that this may need to be adjusted)?

Answer 1

One problem is that "most simple structure" is not well defined; simple structure is based on multiple criteria, and a rotation that is best on one may be bad on another and vice versa. @CHL gave a good summary of the criteria here, listing these five criteria:

1. Each row of the factor matrix should contain at least one zero
2. If there are m common factors, each column of the factor matrix should have at least m zeros
3. For every pair of columns in the factor matrix, there should be several variables for which entries approach zero in the one column but not in the other
4. For every pair of columns in the factor matrix, a large proportion of the variables should have entries approaching zero in both columns when there are four or more factors
5. For every pair of columns in the factor matrix, there should be only a small number of variables with nonzero entries in both columns

and adding:

The ideal simple structure is such that:

each item has a high, or meaningful, loading on one factor only and
each factor have high, or meaningful, loadings for only some of the items.

Well, what if one rotation has a lot of 0s and near 0s, but has many items that load on more than one factor? Or what if it has no loadings that get close to 1?

"Simple structure" is a good goal, but it is a guideline. Since this is exploratory factor analysis, I think another set of criteria (even vaguer than simple structure, unfortunately) is "does this rotation make sense? Does it help me understand the data? Do the factors represent traits I can recognize? Does it give me insight?"