In my working paper, I have some questions about whether I should add some control variables in SEM. Some persons suggest that my paper has lack of control varialbes such as age, education background act as. However I found when I add these variblae (7 variables) in SEM the model fit reduces largely. According to many stuides published in top journal, maybe there are many advantages withouht adding control variables. But I do not know how to say the advantage.
Can you help me to explain how to express the advantage without adding control variables in SEM?
If you add covariates and the fit of your model becomes worse, this suggests a need for direct effects from the covariates to the factor indicators. If they are significant, this indicates measurement non-invariance due to differential item functioning (DIF).
I cannot think of an argument to support not including the observed covariates. By not including them, you are assuming that the latent variables in the model have measurement invariance with respect to those covariates. The fact that direct effects are needed means that you don't have measurement invariance.