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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.

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Factor regressions tend to suffer from the measurement error downward bias. To overcome this, you would need to build a full structural equation model. Sometimes, regression among factor scores may work out, though.

Regression using the principal components also produces biased estimates, as it is an implicit form of regression shrinkage.

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