Will Structural Equation Modeling be reliable if I have two highly correlated variables and I know that they cannot share the same latent variable?

Question

I have two variables which are highly correlated (0.99). But I want to evaluate their individual effect on the target variables (2 in this case). I don't want to create a latent variable using these two variables because logically they don't belong in the same group.

If I use a regression-like model (Y1 ~ X1 + X2, Y2 ~ X1 + X2) in the SEM ( lavaan package in R), will it be the same thing as using multiple linear regression?

Does using structural equation modeling make sense in this case? If not, which would be a suitable method for this analysis?

Answer 1

You'll get the same estimates (and standard errors) as running two linear regressions (assuming that you have covariances between Y1 and Y2, and X1 and X2).

SEM buys that you can do a multivariate test, which you can also do using MANOVA. Apart from that, you don't get very much. Also, you might look at this paper, which talks about how the correlation between outcomes can affect power (it's true for SEM and MANOVA).

The big thing that SEM can buy you is Full Information Maximum Likelihood (FIML)estimates, if you have missing data. If you don't have missing data, you don't care though. And if you do have missing data, you can do multiple imputation, which is asymptotically equivalent. (I find FIML to be quicker and easier - but YMMV, it probably depends what you have more practice at.)