Factor Analysis gives two solutions, one in the space of loadings (correlation coefficients between original variables and extracted factors) allowing you to 'give

a name' to the factors. The other solution corresponds to the factor scores, i.e. to the value of each factor corresppnsnt to your statistical units (rows of your original data matrix, while variables are the columns).

Each row (statistical unit) of the data set aquires a value relative to each of the extracted factors. The statistical units with higher (or lower) score on the factors are the ones more 'typical' (the poles) of the factors.

If you really want to do this you could build a reasonable regression model with a matrix, y holding your factors and x as the IVs from your prefactored variables. Notice that y is a matrix so mutivariate multiple regression is needed. Then using modern variable selection methods NOT STEPWISE PLEASE

should answer your question in some detail. I don't think I would want to know the answer that badly. . But if you do see Wichern and Churchill Applied multivariate Statistical Analysis, in the z-library google instructions for it's use. R would be the easiest way to do this regression. The variable selection methods I would recommend are discussed in the attached paper. Good luck 🤞🤞😃. David Booth PS if you successfully do this please publish the paper.

Thanks, how do I get these factor rows when using the factanal function in R? Paper looks impressive but I woud think that straight up factor analysis is easier

Well factanal doesn't do everything. A variable selection from the pre-factanal IVs is the best I can do to answer your question. Best wishes, David Booth