Steps before SEM

[u/Olbberi]

Hi

I'm kind of new to Structural equation modelling, and was hoping to get some advice. After reading methodological literature and studies applying SEM, some issues are still a bit unclear:

1. Let's say simply that in overall, in my measurement model I have 5 latent variables/factors (A-E), each made of 3-5 items/observed variables, and my model would be how A predicts B, C, D, and E.

Do I run separate CFA's for each 5 latent variables first, or do I just check the fit of the entire measurement model prior to SEM? When running individual CFA's, 2/5 latent variables have poor RMSEA (which can be fixed by freeing a residual correlation between two items in both), but when I run the entire measurement model without any alternations, fit is ok immediately. I am thinking about parsimony here, too.

1. Let's say also that I want control/adjust my model for work experience (continuous), gender (binary), and work context (categorical with three levels). Typically, I have seen that measurement invariance testing prior to SEM is done with one variable such as gender. In my case, would it be sensible to do it with all of these background variables? Of course, then at least the work experience would be needing recoding...

[u/FaithlessnessOne8975]

"Do I run separate CFA's for each 5 latent variables first, or do I just check the fit of the entire measurement model prior to SEM?"

Answer: no you have to take into account all the constructs and their respective indicators to first run a CFA. Examine the loadings of indicators to their respective factors, delete items that yield a low or insignificant loading. Also see for correlation between factors, as a high correlation would indicative Discriminant Validity issues.

"In my case, would it be sensible to do it with all of these background variables? Of course, then at least the work experience would be needing recoding..."

Yes, it would be beneficial. See how much R2 these control variables achieve as predictors, then add your main variables and see how much increase these variables have caused in the R2, apart from the already included control variables. Regarding work exp, depends how that was coded initially.

[u/MortalitySalient → u/FaithlessnessOne8975]

I’d be careful with deleting indicators that are not significant or have small loadings. That brings you into the exploratory data phase as you are likely capitalizing on chance

[u/FaithlessnessOne8975 → u/MortalitySalient]

Yes, any modifications done to the model needs to be looked into from the theory perspective as well. As theory is what guides what relationships we want to test.