Imagine a hypothetical scenario:
You have data a short survey of 9 questions that participants respond to on a continuous rating scale. You suspect that Questions 1-3 assess one particular factor (F1), Questions 4-6 another (F2), and Questions 7-9 a third (F3). You conduct an exploratory factor analysis, which supports your theory of measurement (yes, I know you could skip straight to CFA, but that isn't the point here). But now you want to use the three factors (F1-F3) in an exploratory regression analysis to predict some other variable (let's call it Y). You need to compute scores to represent the three factors, and have one of two broad methodological choices for how to do so.
You simply sum or average the responses for items within a factor (e.g., sum or average the scores of Questions 1-3 to compute a score for F1).
You use some method (e.g., regression scores, Bartlett scores, Anderson-Rubin scores, etc.,; DiStefano et al., 2009) of estimating factor scores for F1-F3.
I'm aware that the use of estimated factor scores has its benefits (e.g., more accurately capturing the true correlations between factors; acknowledging the differential importance of each item for factor makeup via different factor loading values, etc.,) and limitations (e.g., are they even legitimate to use, given concerns of indeterminancy?). But one thing that I am uncertain about is whether using estimated factor scores (Option 2) in such a hypothetical analysis would be a more statistically powerful approach than using sum/average scores to represent the factors (Option 1)?
I know that using Exploratory SEM and traditional SEM methods to model F1-F3 predicting Y would be more powerful than using observed sum/average scores of the factors, but since estimated factor scores are not latent, I am not sure whether their use would confer similar benefits for statistical power. Is there any simulation work on this particular aspect of estimated factor scores?
Any accessible answer and explanation, as well as a key reference or two (if available) would be very much appreciated.
DiStefano, C., Zhu, M., Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation, 14, 1-11.
Grice, J. W. (2001). Computing and evaluating factor scores. Psychological Methods, 6, 430-450.