# Is it possible to produce factor scores estimates that are not centred (factor analysis)?

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?

• FA 99% of time is done on correlation or covariance matrix. That means that the data are centered (variables' means are removed) prior factor extraction. Hence, factor scores cannot have any "original" mean, their native mean is 0. And after all, why would one want other mean, than convenient 0, for the scores? Please explain what mean are you after and why, because your aim is not quite clear. Dec 18 '20 at 21:02
• To repeat again: f.scores are linear combinations of variables, each variable having had its own initial mean. What or which mean then should f. scores of a factor have? Dec 18 '20 at 21:07
• Well, I want to look at FA as a form of matrix decomposition technique. NMF for example, would decompose the original multivariate data to K sub-matrices that their sum would best reconstruct the original data. In NMF for example, I could look at each of the K matrices in their real scale. I wonder if theoretically it is possible with FA. Dec 18 '20 at 21:30
• For classic FA, "original data" are the centered data. It is centering that allows to analyze & explain correlations/covariances. It is possible to apply FA to raw SSCP matrix, why not, but it will not allow to explain correlations. Dec 18 '20 at 21:40
• I don't think it is useful or heuristic to look at FA or even PCA through the NMF lens. Dec 18 '20 at 21:47