Factor, signs, reversed scores and predict

[Nataly Obando Rozo]

When I run in STATA factor v1-v3. I expect v1 contribute negative to the factor and v2 and v3 contribute positively. Something like factor=-v1+v2+v3. However, what I got is totally the opposite factor=v1-v2-v3. In the correlation matrix the correlation between items is as I expected (v2 and v3 positive correlates) and v1 correlate negatively to (v2 and v3), but it seems is in the contribution to the factor where I don't get the sign I am expected. First question, can I use for my analysis either factor or its negative (-factor)? They are the same?

I tried to reverse all the scores of v1, v2, v3 (ie change from 1 to 5, to 5 to 1) but it didn't change the loads to the factor, they remain exactly the same in magnitude and sign, correlation matrix exactly the same. However, what did change were the scores. I mean, when I use "predict" the mean of the factors change of sign but not in magnitude. So, my second questions: How is possible that with the reverse items the load of the factors does not change but the predicted factors do change?

Thanks for your help

[Clyde Schechter]

You have to remember that the factor analysis problem is unidentified. Yes they are the equivalent. The factor loadings are eigenvectors solving a certain matrix equation which I will not reproduce here. If you are interested in the details, look at the Methods and Formulas section of the -factor- chapter of the PDF documentation installed with your Stata. Suffice it to say that the negative of an eigenvector is also an eigenvector.

The factor loadings are really a pure function of the correlations among the variables you are factoring. The actual values of those variables are not otherwise relevant for that. But the factor scores are linear combinations of the actual variable values. When you reverse scored the items, you did not change the correlations among them, but you did change their values. So the loadings remained the same but the predicted factor score did.

[Nataly Obando Rozo]

Thank you so much. It is really helpful.

A last question. I'm trying to replicate the factors that STATA gets after the command predict. What I understood is that I just needed to multiplicate the scores of the variable times the variable to get the factor. Then fx=(0.06*m1x+0.037*m2x+...). However, I don't get the predictor of fx that STATA gets. Do you know how can I replicate the prediction of the factor?

. predict fx
(regression scoring assumed)

Scoring coefficients (method = regression; based on varimax rotated factors)

--------------------------------------------
Variable | Factor1 Factor2 Factor3
-------------+------------------------------
m1x | 0.06808 0.30596 -0.02712
m2x | 0.03759 0.24859 -0.01583
m3x | 0.11616 -0.00055 -0.04090
m4x | 0.37636 -0.05444 0.04460
m5x | 0.09136 0.23596 0.00839
m6x | 0.03478 -0.00299 0.32201
m7x | 0.35751 -0.05103 -0.01257
m8x | -0.01383 -0.02607 0.33150
--------------------------------------------