# Correlation of latent variables: Sum-scores vs. SEM correlation

I use a set of about 20 attitudinal items and confirmatory factor analysis (CFA). Loadings and model for are sufficient. In the next step, I want to test for correlations between these latent factors. I calculate factor scores based on the CFA. And here comes my question: If I calculate correlations between these factor scores, correlations are quite high (up to .7). If I calculate sum scores (adding up the items) and correlate these scores I get only a medium correlation. How does this come? I am aware that the latent factor in the CFA are weighted while the sum scores are not. However, I do not think that this can be the reason for the different correlations.

General framework: N > 8000, Likert scale, attitude items.

This is a similar topic, but does not on the possible differences between the two methods. Correlational study or ordinal data using 5-point Likert scale

edited to make the question more clear

• Confirmatory factor analysis suggests a high (standardized) correlation (0.59, -0.45) for 3 latent factors. How to understand this passage? Moreover, you extracted factors in EFA as orthogonal. Why are allowing them to correlate afterwards? – ttnphns Oct 24 '14 at 11:12
• In the CFA model I added a covariance between the latent factors to check, if these constructs are independent. From the theory it is not reasonable to suggest that these latent factors are uncorrelated. You are right, in this case I can use another rotation. But this does not change the results a lot. – ChristopherB Oct 27 '14 at 9:55