st: Testing a curvilinear mediator

["Dirk Deichmann" <dirk@dirkdeichmann.de>]

Hi group,

I would like to test a model with a mediating variable which by itself has a curvilinear relationship with the DV. IV and DV are binary variables whereas M is continuous.

If such an analysis of a mediator, which is curvilinear, is possible, how can I perform it? Are there some causal steps I need to go through? 

I thought that maybe a moderated mediation would work except that the moderator is not a different variable but the same as the mediator.

I started with the four step procedure and added the squared term in step 3 next to the linear term, and the IV (see steps and findings below). However, I have read that for moderated mediation it is advised to also include an interaction of the moderator with the IV in the first step already. But this seems not really applicable in my case, or did I misunderstood something? 

Provided that I am doing something reasonable here, how do I actually interpret a curvilinear mediator? Is it correct to say that the mediator works best at intermediate levels and less at low and high levels if I find an inverted U-shaped relation? Also, how should I perform the Sobel test? Does this make sense at all if my mediator turns out to be inverted U-shaped?

Path	b	(s.e.)	sig.
Step 1: IV > DV	0.63	(0.36)	^
Step 2: IV > M	0.25	(0.14)	^
Step 3: M > DV (controlling for IV and M squared)	1.84	(0.38)	***
Step 3: M squared > DV (controlling for IV and M)	-0.50	(0.15)	***
Step 4: IV > DV (controlling for M and M squared)	0.44	(0.38)	n.s.

Lot?s of questions- I hope that somebody knows something about this and would like to thank you in advance for your kind help and support. 

Best,

Dirk


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