I'm trying to figure out if this makes any sense: I have a composite index, "X", created from a set of categorical exposure variables (let's call them "Ei") based on their association with the mediator, M, using multiple correspondence analysis. Can I perform SEM with X as the exposure, M as the mediator, and Y as the outcome (X --> M --> Y)? X would be an unobserved variable while Ei and covariates will be observed. How do I measure the direct and indirect effects?
Alternatively, if I were to perform a mediation analysis on Ei --> M --> Y, can I still use SEM with Ei (the individual component variables of X) as the exposure?
Thanks!