I am currently running a SEM in Mplus 7.0. In this, I have four independent latent constructs, measured by 4, 4, 4 and 10 variables. The latent constructs correlate .67-.80. These constructs should indeed be highly related; one is an older construct used in a lot of other research, the other 3 are theoretically distinct subdimensions of a closely related yet different construct. CFA supports this. Raykov composite reliability for all measures is high, .75-93.

I simultaneously linearly regress a number of other latent variables on these independent constructs, while allowing covariance between the predictor variables. Estimation uses MLR since I have non-normally distributed variables.

Running such a model has reasonably low explained variances (R^2 between .25 and .50, with an extreme case of .06), and in some cases some quite unexpected results (e.g. negative sign where a positive would probably be expected). While I have heard that sign reversal can be symptomatic of multicollinearity in non-SEM regression, I do not know if this is also a concern for SEM. I have also failed to find much literature on the topic, but what I have found tends to suggest only that standard errors would inflate, thereby leading to type 2 error. The sole simulation study I found suggested that under high composite reliability and sample size, the probability of this is strongly reduced (Grewal, Cote and Baumgartner, 2004).

Should I nonetheless be concerned that these results are indicative of too strongly multicollinear variables?


First, I wouldn't call an $R^2$ of between 0.25 and 0.50 low.

Now on to the question. (Multi) collinearity is a weird thing. It's described as a symptom, but it is not. It's what regression is supposed to do, and when you regress variables onto other variables, whether they are latent or not, you are essentially doing regression.

If you want to know whether the correlations between predictors are changing sign when you do a regression, just allow all your latent variables to correlate. This is the saturated measurement model. Then switch to a regression model. If all your endogenous latent variables are regressed on all of your exogenous latent variables, then all you have done is a transformation of the correlation matrix. If there are restrictions, then the two models are nested. You can compare the correlations (or covariances) with the regression parameters to understand what is happening.


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