How to interpret a two-way interaction in a 3-way interaction model I am trying to predict y with variables a, b and c. I have two models and I get different results depending on how I fit my model.
Model A is the simpler model, in which I exclude variable c. In model B, I include all main effects and possible interactions between the 3 variables. I am interested in the ab interaction that is bolded.
In model A, there is NO significant ab interaction. 


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*Model A: y ~ a + b + ab
In model B, there is a significant ab interaction, and the abc interaction is significant as well. 


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*Model B: y ~ a + b + c + ab + ac + bc + abc


Everything has been coded properly, such that the variables are mean centered or effect coded. This is a generalized (logistic) linear mixed effects model fit using glmer in R.
My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details of the model? Why does adding a 3-way interaction make an originally non-significant two-way interaction (model A) significant (model B)? 
 A: 
My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details of the model? Why does adding a 3-way interaction make an originally non-significant two-way interaction (model A) significant (model B)?

Neither model is "correct". They are different models. It is absolutely OK to find a meaningful interaction in the first model, but the same interaction may not be meaningful in the second. In the second model, the a:b interaction itself is involved in an interaction with c. This means that the intepretation of the a:b interaction in the second model is conditional on c being zero (or at it's reference level if it is categorical). It is then necessary to intepret the a:b:c interation, which will tell you how the a:b interaction changes with c. So from this it is easy to see there is no reason to expect the a:b to have a similar magnitude (or statistial significance) in the two models.
