Does anybody know how to calculate the maximum likelihood factor loadings from only the correlation (R) matrix and/or covariance (S) matrix in Factor Analysis "by hand" (i.e., by Excel)? Or, even better, point me to a clear explanation with a worked example?
I don't have the underlying data, so I can't just use a software program to solve the problem for me. (Any answer involving typical FA software commands or menu sequences won't be helpful, I don't think.)
To the extent it's helpful, I'm using Johnson and Wichern's "Applied Multivariate Statistical Analysis", 6th Edition. In the exercises in Chapter 9, we're given just the R or S matrix and then asked to perform the maximum likelihood calculation repeatedly (e.g., exercises 9.20 b; 9.24, 9.26, and 9.27), yet the book never shows an example (as far as I can tell, nor does the answer key, which my professor makes available to us).
Thanks in advance and regards!