Specifying observed variables as endogenous in SEM?

[Andrew Walton]

I could really use some help figuring out what I'm doing wrong with a simple SEM model that involves two latent variables ('SALIENCE' and 'COMMITMENT') and two observed variables ('dif_score' and 'grade'). Latent variable SALIENCE is endogenous and has four indicators (sal_1, sal_2, sal_3, sal_4). Latent variable COMMITMENT is exogenous and has seven indicators (cmt_1 - cmt_7). I wish to specify three structural paths in all: from COMMITMENT to SALIENCE, and from COMMITMENT to the two observed variables. The problem I'm having is that Stata views my paths from COMMITMENT to the two observed variables to be part of the measurement model (that is, as additional indicators of the latent variable) rather than as paths in the structural model.

Is there a way to specify that simple observed variables should be treated as endogenous outcome variables, and therefore part of the structural model? Whether I use command syntax or the model builder, Stata treats the observed variables the same way, by assuming they're additional indicators of the latent variable COMMITMENT. Any help you can provide will be MUCH appreciated!

Here is my command syntax:

sem (SALIENCE -> sal_1 sal_2 sal_3 sal_4) ///
(COMMITMENT -> cmt_1 cmt_2 cmt_3 cmt_4 cmt_5 cmt_6 cmt_7) ///
(MGR_Salience <- Affective) ///
(dif_score grade <- Affective)

[Clyde Schechter]

I think you're trying to make a distinction without a difference, as they say. Based on what you describe, cmt_1-cmt_7 and the two observed variables (which you do not name and which do not appear in your command syntax) are all variables for which COMMITMENT is an "input." From a mathematical point of view, all 9 have indistinguishable roles. You may choose to think of cmt_1-cmt_7 as the measurement model and the other variables as part of the structural model, but that is purely your mind's point of view and has nothing to do with the mathematics of it.

In fact, try to think of it from "Stata's point of view." How would Stata know that the two observed variables are part of the structural model but cmt_1-cmt_7 are part of the measurement model and not the other way around? There is nothing in the equations that distinguishes these things.

[Andrew Walton]

Thank you, Clyde, for your quick response and input. My mistake! I posted the wrong bit of syntax; it should read:

sem (SALIENCE -> sal_1 sal_2 sal_3 sal_4 sal_5) ///
(COMMITMENT -> cmt_1 cmt_2 cmt_3 cmt_4 cmt_5 cmt_6 cmt_7) ///
(SALIENCE <- COMMITMENT) ///
(dif_score grade <- COMMITMENT)

What I refer to as the 'measurement' model are the first two lines with my latent variables in caps, while the 'structural model' consists of the second two lines. The two observed outcome variables are 'dif_score' and 'grade', and I have hypothesized significant relationships between COMMITMENT and each of these. Now, I think I understand what you're saying in that I can interpret the significance of the path regardless of whether Stata labels it 'Measurement' or 'Structural'. But, what I left out for the sake of simplicity is that I plan to also run this as a multi-group model in which I add a male/female categorical grouping variable so as compare model fit across the two groups. When I run this as a multi-group SEM model, in order to establish whether my measurement models are invariant, I will need to ask Stata to constrain my measurement coefficients to be equal. In this case, I will not want the two outcome variables to be constrained as well. Am I still wrong to see this as a problem?

[Clyde Schechter]

Ah, that puts it in a different light. And with the use of the -ginvariant(mcoef)- option you would indeed end up with the coefficients for dif_sore and grade_ on COMMITMENT constrained to be equal across groups.

But you can get around that. Use -ginvariant(none)- and then individually spell out the constraints on all the terms in the measurement model as you conceive of it. There are examples of this in the manual chapter on SEM. (If you are using Stata version 15, see page 90 of the SEM manual.)

[Andrew Walton]

Really appreciate the help -- I'll look into how to do it by specifying individual constraints. Thanks a lot!