I've previously asked this question - on how to obtain factor scores that are not z-standardized, but have their true factor variances, and got a great answer.
However, I would still want to look at each of my factors also with its relative mean (infer the right portion from the means of the measured variables). All conventional methods that compute factor scores return z-standardized scores - having unit variance and zero mean.
I've read in one place that Thompson's method for computing factor scores can calculate standardised scores (unit variance) with means that are determined by the original variable means. In other places I see that the 'Thompson' method is the same as the 'regression' method.
My question is - can I estimate such factor scores? Do I just need to infer it from the "beta" coefficients?