What are the assumption of the moderated moderation model?

Question

I'm running a moderated moderation model (model 3 of PROCESS macro for SPSS) in order to explore a three-way interaction, with one independent variable (A), one dependent variable and two moderators (B, C). I was wondering if are there some assumption to be considered, such as if the significance of the direct effect of A on the dependent variable or other two-way interactions are needed. If not should I consider the model valid if only the third level interaction (ABC) is significant? Thanks

Answer 1

"Moderation" is just a synonym for interaction in a linear model. I don't use SPSS, but I infer that this is a model including all individual coefficients for A, B, and C, all their two-way interactions, plus their 3-way interaction.

The issue of whether the model is "valid" has more to do with whether the underlying linear-modeling assumptions of linearity and a proper distribution of error terms hold, and whether you have avoided overfitting the data. If the coefficient for the 3-way interaction term ends up not being "significant," it just means that you couldn't document its "significance" by the usual criterion with your data set. That doesn't make the model "invalid," just perhaps more complicated than ended up being necessary.

Do NOT try to interpret "direct" or "main" effects of a predictor involved in an interaction from its single-predictor coefficient, as you seem to have in mind. The value and apparent "significance" of such an "effect" depends on how the interacting predictors are coded. See this page for a simple example with a 2-way interaction.