We are having a mediation model with 2 outcome variables, one mediator and one predictor (exogenious). Based on the literature all of the paths are relevant, therefore we are having a just identified model (with no fit indices of course). We used SEM mainly, because the relationship of the 2 outcome variables is important, and it can easily be handled by a path model.
My questions:
1. What are the disadvantages of using SEM here? (besides, that we are not using the full potential of model fitting with the data)
2. If I am not mistaken, we are going to get the same results as applying standard mediation analysis. Is this correct? Can we reference any specific paper, which is dealing with this problem?
3. What other solutions we can have than using two separate mediation models for the two outcome variables?
Marton,
Just to be sure, I would have a look at this:
Article The Mediation Myth
Article Guidelines for the Investigation of Mediating Variables in B...
Hi Marton,
in addition to the notes by Heiko, my 2c are:
1) You only have a just-identified model if you freely estimate the direct effects of the IV on both outocmes. In most cases this will be reasonable but you should think about that. If you have a strong mediator, a full mediation hypothesis may be reasonable and valid. The difference between full and partial mediation terms of causal support is dramatical which Kline's mediation myth paper illustrates.
2) The fact that you only have one IV sound a bit questionable. That is, you assume no confouding of the x - m link as well as no confounding between both m-y links. Perhaps, you can think of some reasonable control variables. Incorporating these with specific effects also serves leading to positive df and may enable testing the model in general as well as specific effects.
Perhaps you can even identify variables which are related only to x or m and, hence, function as instrumental variables.
Best,
Holger
As outlined by the previous answers, just continue with your analysis. By the way, any multiple regression formulated as a SEM is saturated so that's not really an issue.
More importantly, you need to calculate the indirect effects properly (the product of the coefficients along the indirect paths) and you need to bootstrap the standard errors of the indirect effect (because products of normally distributed variables are not normally distributed any more).
See here for a simple example:
http://lavaan.ugent.be/tutorial/mediation.html
For references, you should look for Andrew F. Hayes. You will find much of the relevant literature by going through his work.
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