SEM: Collinearity between two latent variables that are used to predict a third latent variable In some structural equation models that I use in my bachelor thesis, there is a substantial
correlation between two latent variables that are used to predict a third latent variable.
Now I know there are several ways of quantifying multicollinearity when it comes to observable variables, but what about exogenous latent variables? 
Can I simply use the same indices that I use for observable variables in regressions analysis (such as the VIF)? And are there any guidelines as to when collinearity between latent variables becomes a problem?
I would really appreciate your advice!
 A: Rules of thumb may say that multicollinearity is a problem only if two variables correlate above, say, .9 or even more. If two of your latent variables correlated that much, or even in the range of .7 / .8, then you have a problem before it comes to predicting the third variable: Your measurement model seems to be not very well defined. Maybe, for example, the two latents would be better modeled as only one? I would care much more about the measurement model then about multicollinearity.
A: Latent variable models are simply used to attempt to estimate the underlying constructs more reliably than by simply aggregating the items. Thus, in the structural part of the model (i.e. the regression) the same issues apply as in a standard regression.
Apart from in extreme situations (e.g., a standardized regression coefficient greater than 1), there are no definitive cutoffs. But cutoffs can be interpreted as for standard regressions. Some suggest a VIF of >5 or >10 as problematic, for example, but it these numbers would be extremely lenient if you were interested in the effect on one variable on the DV after controlling for the others (https://doi.org/10.1081/QEN-120001878).
One thing to note is that although calculating a VIF is easy in a standard regression and many packages/programs will do this automatically, it is not easy in a latent variable model. The calculation of VIF for a variable requires regressing it on all other predictors in the regression, which in a latent variable model means this has to be done in a latent variable model. As a result of this complexity, it is not surprising that this cannot be easily automated (and as far as I am aware has not been done).
Note also that multicollinearity is actually more likely to be an issue in latent variable models than when you just add items together since you are greatly reducing the error included in the estimate and thereby increasing correlations between related constructs.
What to do if you detect problematic multicollinearity will vary on a case by case basis. In most cases, it would probably be advisable to alter the measurement model, but there may be cases where such a course would not make sense. In such cases, you would probably be advised to drop one or more variables instead.
