How to obtain uncentered factor scores from Factor analysis The Exploratory Factor Analysis has the following mathematical formulation as in the screenshot from wikipedia (https://en.wikipedia.org/wiki/Factor_analysis):

That means the factors in F are centered to zero and the mean values of the observations are in X.
For my analysis, I would like to compare the resulting factors including the mean values, such that they may be compared in their magnitude with respect to X.
This is:
X = L * G  + e
where G would contain the factors including the mean values aka "uncentered factors scores"?
Does this make sense and if so how is it possible?
It occurred to me that in implementations such as https://factor-analyzer.readthedocs.io/en/latest/_modules/factor_analyzer/factor_analyzer.html#FactorAnalyzer.transform doing so is not an valid option.

For the use case of interpreting the resulting factor scores with a "the higher the better" interpretation, we could use the (usual) factors scores using the centered input data.
The resulting factors scores using the centered input data are on the same scale regarding their mean values and variance.  Therefore, we can compare the direction and magnitude of the factor scores directly with regards to the loading matrix.
The sign of the factor scores and loadings can jointly change for each factor without impacting the outcome of the factor analysis but only the interpretation of the factor scores and loadings.
Therefore, we may determine the signs of the loadings by setting the absolutely largest loading of a factor to a positive sign and changing the signs of the other loadings of this factor if necessary accordingly.
Ideally, the (absolutely large) loadings of a factor all have the same sign, in our case a positive sign. If they do, we can interpret the factor scores for a single observation in terms of their size, in our our case with the interpretation that more positive scores are more relevant to "explain" the positive values of the observation.
