moderated mediation with multiple group analysis

[ahmad]

Hi,  

How can I test a moderated mediation model in lavaan, where I have a mediation model (X → M → Y) with a continuous moderator, and also want to examine whether this model is applicable across another grouping variable with 4 levels, using SEM and multi-group analysis? I would appreciate any advice on an appropriate analytical strategy.  

Best,

A

[Jeremy Miles]

I think we need a bit more detail on the nature of the moderator. 

If the moderator affects the X -> M relationship, or the indirect effect (X -> Y) this is relatively straightforward - treat it as you'd treat a moderator in regression. If the moderator is continuous and hypothesized to affect the M -> Y relationship, this is much more difficult.

If you have another possible moderator with 4 groups, this is (relatively) straightforward as a multiple groups model. If you expect both moderation effects to be happening simultaneously, that's a huge and complex model, with a lot of tests.  In addition, if you don't have a vast sample size, you're going to have very little power to detect these effects.

One rule of thumb that I like is Abelson's 42% rule. That is, if you have an effect that is statistically significant in one group, and p = 0.05, if you have another group and you expect a moderator effect, you need the size of the effect to be 42% of the magnitude of the first effect, and in the opposite direction. So if you have a correlation of 0.4 in one group, with  p = 0.05, and you expect it to be lower in the second group (which is the same size), the effect will need to be -0.168 in order to be statistically significant. A moderator that reverses the direction of an effect is pretty unusual.

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