I have used 20 variables to extract 4 factors in a factor analysis. Now I want to use the extracted factors (factor scores) as IVs on an outcome variable. Besides I want to include 4 other variables as IVs in the regression which were not used in the factor analysis. That means I want to regress 4 factors and 4 variables (from outside of the FA) as IVs on a DV. Is there any problem in it statistically?
Secondly, if I want to run a separate regression on another DV by using only 2 of the factors (factor scores) and 3 other variables as IVs, is there any problem?
Just to know, if I extracted 4 components from a PCA (Principal Component Analysis) instead, what would be the answers to the same two questions?
Grateful for any help.