# Does the use of EFA factor scores (vs. sum/average scores) impact statistical power of subsequent analyses?

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.

Option 1

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).

or

Option 2

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.

The Question:

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?

As of my current reading, this question is not addressed in Grice (2001), DiStefano et al., (2009), or the questions here, and here on CV.

Any accessible answer and explanation, as well as a key reference or two (if available) would be very much appreciated.

References

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.

• But it seems that you haven't disclosed statistically what sort of "statistical power" you suspect to be affected in the regression scenario. Factor scores, albeit approximations, can be seen as better or fine-tuned approximations to what the concept of latent factor implies than mere sum/average. Then, what can be expected to be a more "powerful" predictor in most general sense - a fine measure or a crude measure? Commented Jun 20, 2016 at 17:20
• I'm interested in the power to detect significant regression slopes (assuming true associations in the population) for F1-F3 predicting Y, assuming all else (e.g., sample size) is equal between the two approaches. Will you have a better chance of rejecting the null for each Wald test of each slope, and/or the omnibus test of whether the model predicts zero variability in Y, when using estimated factor scores vs. the average or sum scores? Commented Jun 20, 2016 at 17:30
• In an answer here I mentioned some of reasons why sum/mean score is still used despite factor scores are computable. One of the reasons is that (traditional) FA model assumes quite narrow paradigm of "latent trait". Psychological trait or construct could be theoretisized not only that way. For example, it could be thought of as a cluster of prototypical roles (behaviours). If so, reason to estimate scores would be weak. (This comment is not a response to your last comment) Commented Jun 20, 2016 at 17:35
• Thanks for the additional information, though this post also doesn't speak to the question at hand (though I understand it may be an important limitation of estimated factor scores) Commented Jun 20, 2016 at 17:39