Hello Xenis,

it does not matter whether to specify fixed.x as random or fixed. I prefer using random, as your outcome will present variances, covariances of the indepentent variables and their test statistics. Usually I want to know these.

With regard to the other question: You have saturated model structure with 0 degrees of freedom. Such model always fits the data perfectly and hence you get no model chisuare test (which tests overidentifying restrictions) and maximum fit indices. But, all of this is not informative. Sorry to be so bold, but a saturated model provides only weak evidence for the causal interpretation of your coefficents. Perhaps you can improve that be including variables with specific effects.

Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37(4), 202-213. doi:10.1080/01973533.2015.1049349

Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21, 1086-1120. doi:10.1016/j.leaqua.2010.10.010

Best,

Holger

Thank you for your detailed answer!

You are right, my mediation model is of course not very valid without checking the causality. Since it is a secondary analysis, I unfortunately did not have much flexibility in the study design.

What exactly do you mean by variables with specific effects? Are you referring to specific and non-specific factors of psychotherapy?

And thanks for your literature suggestions!

Hello Xenis,

I meant, any variable that has only an effect on either the exposure variable or mediator but not on downstream variables. These are called "instrumental variables" and can enhance the causal interpretation of some effects. For instance, if you have a partial mediation model and a further variable w --> m then you get a model test that will fail when either w affects y, too OR when y causes m OR when the m-y effect is affected by unobserved confounders. Or turned around, a fitting model is a stronger support (than the simple partial mediation model) that m causes y and the effect is unbiased. This "mechanism" holds for all variables in a model: If you can identify a variable that has a solely effect on the target variable, the effect that the target variable emits on downstream variables (i.e., variables right to it) get more solid.

Best,

Holger