Hi. I notice that when we conducting path analysis or SEM, if we want to add correlations between an endogenous variables, such as a mediator with other control variables, what actually happened is the correlation between residual error of that mediator correlated with control variables. (Please confirm if my understanding is correct).

I was wondering why we do this, instead of simply use the mediator? Any statistical constraint that I did not realize underlying this approach? Many thanks!

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