I am very inexperienced in SEM. I am testing a moderated mediation model with two serial mediators (M1 and M2) of the X-Y relationship, and also one moderator (W) of the X-M1 relationship (a pathway). The model fits very well. I now want to add two control variables to the model I am not sure how to do this within this relatively complicated model? Can someone advise or give an example?
To obtain valid inference in an SEM model, the residuals for each of X, Y, M1, and M2 must be conditionally independent of the confounder variable(s) to eliminate its/their confounding effects. The easiest and most typical way to do this is to add a path from the confounding variables to each of these variables. However, this will not work in all scenarios. It is unnecessary to add a path if the causal model believes that any one of those variable(s) are independent of the confounders. Adding these paths can cause some forms of bias if the confounders are actually colliders, if there is reverse causality, or if other aspects of the causal model are misspecified such as with variable omission and strong departures from linear relationships.