# Problem regarding the scale and range of factor variables generated in CFA (Stata)

I ran a confirmatory factor analysis in Stata using the sem command. The idea was to extract two factors: TRUST, extracted from four variables measuring the trust towards different groups of people (friends, strangers etc.) on a scale from 1 to 7; SELF-RELIANCE, extracted from four variables measuring the consent of the test-subject regarding statements declaring socio-economic self-reliance as a virtue in our society on a scale from 1 to 4. I intend to use SELF-RELIANCE as a dependent variable in a multiple linear regression. TRUST will be one of the predictors in said regression.

I get pretty decent factor scores, have a decent model fit, everything seems fine. But then I try to generate the factor variables TRUST and SELF-RELIANCE from the PCA using

predict <varname>, latent(factorname)


I expected the factors to have the same scale as their endogenous variables (1-7; 1-4), but they have a range from -2.944997 to 1.157046 (in the case of TRUST). What does that even mean? Did I use the wrong predict option?

My professor said the variables with the constrained factor scores in sem serve as the scale template for the factors, so I don't understand why my generated variables would have such a weird scale. Does anybody know what this means?

Here's my syntax for the CFA (names are in German, as am I, so I'm sorry if I formulated something wrong):

sem (vertrverw vertrfreund vertrbek vertrfremd <- VERTRAUEN) (einkuntmot ranguntakz sozuntger <- EIGENV)
estat gof, stats(all)
estat mindices
predict VERTRAUEN, latent(VERTRAUEN)
predict EIGENV, latent(EIGENV)


In general, Stata predicts the results of factor and principal components analyses as having zero mean. You can check this directly by

summarize VERTRAUEN


Look also at what is reported for the standard deviation.

Nothing stops you re-scaling your new factor if you so wish, but it won't make interpretation of your regression any easier, and it will be an extra step you will need to justify and explain in any paper, report, dissertation or thesis.

As you are asking this, you seem to be at a stage where you need to do much more reading about these methods and even the basic terminology. I have edited your question trivially, but I've let stand your use of both confirmatory factor analysis and PCA. What you are doing is not PCA.

• Thank you Nick, that was very helpful. I suspected as much (and summarized the factors), but was confused: In an earlier analysis using SPSS (a few years ago), I'm relatively sure my extracted factor had the "right" scale (meaning something like 1-7). But that was a EFA, so whatever. I'll do a few days of closer reading before I start with actually writing anything down. Thanks again! – Quadzar Jun 1 '13 at 10:59