Question So, I’ve done my factor analysis. Beyond characterizing the structure of the variables, or maybe doing regressions at the latent level, how can I use these factors? For example, what if I wanted to have estimates of each person’s scores on the unobserved latent constructs (factor scores) and use those scores as IVs or DVs in other analyses (e.g., ANOVA, regression).

Answer This is fairly easily accomplished. We need to get the factor scoring coefficients, and use those to generate factor scores for each individual We’ll start with AMOS, but then generalize to SPSS

Start with a basic factor model

Be sure to request factor scoring coefficients

It will show up in the output

Now, go into SPSS and save the measured indicators as z-scores

Now, write compute statements that turn the Z-scores into factor scores, using the AMOS weights

Now, you’ll get estimated individual scores for each subject in your dataset, representing our best estimate of their score on the unobserved latent constructs.

This approach is sometimes called “regression-based factor scores” It has the advantage that it usually reproduces closes the pattern of factor correlations observed in the factor analysis itself. For example:

 Amos estimates

Some people don’t like these regression-based scores First, they let variables that don’t really load on the factor define that factor’s factor score E.g., WBNCE AND CANCE load on the non-verbal factors too This is done to get the right level of factor intercorrelation in the factor scores Factor score weights tend to be sample-specific, and may not necessarily generalize to other samples They’re a bit cumbersome (Zscores, write equations, etc.)

A simpler alternative is the “unit weighted composite” Unit-weighted means: Each variable on the factor contributes equally To achieve this, each measured variable is converted to Z-scores (we already did that), and then you just take the simple average of ONLY THOSE VARIABLES THAT LOAD ON THAT FACTOR We’ll demostrate that be creating Uspeed, Uverbal, and Ureason (U stands for “unit-weighted)

This will produce unit-weighted factor scores that are not quite identical to the regression-based ones, and that aren’t quite as well-correlated as in the AMOS program. BUT…they’re quickly made and easily replicated across multiple samples that have at least configural invariance with your sample

 Amos estimates

 Amos estimates

Unit-weighted composites will tend to be fairly well related to regression-based factor scores, but The intercorrelations among the unit-weighted composites will tend to be lower than the actual estimated factor correlations in programs like AMOS

Which to choose? There really isn’t a clear basis for picking one over the other. If you want to preserve the intercorrelations among factors, regression-based is best…with the limitations of sample-specificity Just be sure to DESCRIBE which type (regression-based or unit-weighted composite) you chose to use These factor scores can be IVs or DVs in other analyses. Of course, you could probably also do a lot of these other analyses as SEMs … circumventing the whole need for factor scores.

What about in EFA? You can do the same thing in EFA If you conduct the analysis entirely within SPSS, you can even save a step. Let’s rerun the exact same analysis as an EFA

1=Reason 2=Speed 3=Verbal

Same kind of thing as in AMOS 

The factor scores appear magically in SPSS…you just need to keep track of what they are

Reason Speed Verbal

How related are these exploratory factors?

Verbal Speed Reason Verbal Speed Reason Because the SPSS factor solution agreed so nicely with AMOS, the factor scores are nicely related to AMOS-regression based and unit-weighted factor scores. Also, the correlation among SPSS factor scores pretty closely matches the latent factor correlations in either AMOS or SPSS