I have a linear mixed effects model (say AxBxC), where all of the 2-way interactions are significant but the 3 way interaction is not, and I want to perform post hoc contrasts on the 2 way interactions (e.g. AxB). I've found several recommended methods: 1) create a new linear model y=AxB and perform contrasts on AxB using glht. 2) create a new linear model y=AxB and perform contrast on AxB using emmeans. 3) use the original model (AxBxC) and perform contrast on AxB using emmeans.
So far they all seem to give very similar results, but I'm wondering how they are different, and which method is preferred (or if some other method not covered is better).