Correlate endogenous variables in SEM?

[Adam Landon]

Is it possible to correlate endogenous variables in STATA SEM? The documentation says that "endogenous variables are never directly correlated, although their associated error variables
can be." In other SEM software like LISREL or M+ this is an option. Can anyone offer an explanation as to why, maybe I am just missing something here. Thanks.

[Dick Campbell]

I think you may be missing something. By definition, an endogenous variable, latent or otherwise, has an error term. You can specify a model in which those error terms are or are not correlated. . The correlations among endogenous variables are a function of (a) the correlations among the exogenous variables which determine the endogenous variables, (b) the estimated effects of endogenous variables on each other (if any) and (c) the correlations among the error terms (if any). The point is that correlations among the endogenous variables. whether directly observed or latent, are a function of other parameters in the model and are not estimable parameters themselves. See Example 8 in the Stata SEM manual.

I haven't used LISREL in a long time, but I am fairly certain that both there and in MPlus, you can't do what you describe, that is, you can't specify correlations among endogenous variables as model parameters but you can ask for estimates of those correlations as additional output. I am not sure if Stata's SEM provides this information as an option. You can find matrix formulas for estimating the correlations in Ken Bollen's book, Structural Equation Models with Latent Variables.

Note: The MPlus control language is written in such a way that you may think you are specifying correlations among endogenous variables but you are not. A careful reading of the manual will tell you that for endogenous variables you are actually correlating errors in equations. See Mplus Example 3.11.

[Adam Landon]

Thank you for the clarification this helps a ton.

Cheers,

-Adam