how to interpret insignificant 3-way interaction with two significant 2-way interaction?

Question

I have a non-significant 3-way interaction (A X B X C mixed design, 2 binary (A/B: 0,1) and 1 continuous:C), alongside with two significant 2-way interaction(A X C and B X C), and my questions are,

1. should I interpret the results from the 3-way interaction output, or should I run new analyses for the two significant 2-way interactions separately and interpret these instead?

2. my instinct about the first question is to interpret the original 3-way output because it estimates the two 2-way together, even if the 3-way is not significant, if this is the case, e.g., when decomposing A X C by the /EMMEANS command, should i specify the estimation at which level of B or simply ignore it (see the pic below)? If variable B were continuous, could I ask for estimating at mean level of B (the last line in the pic)?

Answer 1

The interpretation here is that the slopes for the equation where $C$ predicts $Y$, the dependent variable, are different for group $A=0$ compared to group $A=1$.  And, the same is true for the slope when comparing groups $B=0$ and $B=1$. However, the differences between your four groups (A0B0, A1B0, A0B1, A1B1) is entirely captured by these two (main effects) comparisons. That is to say, there is not necessarily a different slope for all four groups (the interaction).

My suggestion would be to first rerun the model dropping the insignificant interaction terms (which sounds like $A\times B$ and the three-way interaction). If the parameters estimates for the significant factors are essentially the same for the two models, use the more parsimonious model to report your findings. (Others may disagree with this strategy, but this is standard convention in most social sciences; if your discipline has a different convention...it would be best to adhere to that.) But to clarify, this means keeping the interactions all together in one model.