Let's suppose I have model with three latent variables (L1, L2, L3). These three latent variables are included as regressors in a path explaining Y (a measured variable), so the equation would be: Y =~ L1 + L2 + L3.

The survey was gathered in three different cities (City_A, City_B, and City_C) and I have theoretical reasons to believe that regression coefficiente for L3 should be different.

Now, in standard econometrics or statistics the intuition would be to add interactions. The Equation would be:

Y = L1 + L2 + L3 + City_B + City_C + L3City_B + L3City_C

Where City_A was used as the reference variable and the "effect" is just L3.

My first equation is if in SEM, that apporoach is still valid.

As I cannot add interactions with latents in lavaan and STATA is extremely slow, there are two alternatives I am considering. The first is to run a Multigroup SEM by city setting everything to be the same except for the path of L3 on Y. That way I will get three estimabes of the L3 coefficent: L3_A, L3_B, and L3_C.

My second question is if this approach is correct or even preferable than the interactions. Moreover, I am wondering if both models are the same. An additional issue I am considering is if I should evaluate invariance of L3 for the multigroup to make sense. The reason why I think the effect of L3 on Y vaies by city is because the construct is probably perceived different in every city.

The second alternative I am considering is to run a CFA with L1, L2 and L3, and take out the scores for the three variables. Then I can run a regression using L1, L2, and L3 with the city interactions. I have read some papers where authors follow the mentioned approach but using EFA or PCA, I prefer CFA.

My third question is if I should stick to the multigroup alternative or go with the CFA + linear regression.

New contributor
Orlando Sabogal is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

Your Answer

Orlando Sabogal is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.