I have a very elementary question. I'm working on a two-level SEM in Mplus 3.1. I'm finished with the CFA of my measurement model. Turning my attention to the SEM, when I substitute causal paths for correlations among the 3 latent constructs at the within level, the model no longer reports standard errors or standardized coefficients and has several error messages.
Before burdening you with what is perhaps idiosyncratic to my data and model, is there something more systematic I should be telling Mplus when going from CFA to SEM? As it stands, all I've done is add the commands (f3 on f1 f2; f2 on f1;) to the CFA model %within% statement in which f1, f2, and f3 were free to correlate. That's it.
My question concerns the between-level part of the regression (fb1 fb2 fb3 on K). From the correlations I know that K has a very strong (r = .90) positive association with fb3, and a very strong (r = -.90) negative association with fb2. And, fb2 and fb3 are negatively correlated as well (r = -.89). Fb1 and fb2 are correlated at -.44. When K is included in the model, then residual correlation between fb2 and fb3 becomes nonsignificant (-.09), and also residual correlation between fb2 and fb1 becomes nonsignificant.
1) What can we conclude from that (i.e., correlation between the factors disappears when K is included)? It especially concerns fb2 (its residual variance and residual correlations become nonsignificant). Does it mean that some of the associations between the factors can be totally explained by the factor K? Does it mean that the association between fb2 and fb3 is somehow spurious?
2) If the residual is significant (for instance for fb1), I assume this residual is "latent" (it does not include error any more)?