Plotting interaction effect without significant main effects (not about code)

Question

This is not a question about implementation:

I have a GLMER model with a significant three way interaction. Neither of the two way interactions or main effects are significant. I accept this model and leave all lower order effects in the model, but want to plot this three way interaction: x, y, and then z as colour in a ggplot. I predict responses of y based on data I generate for y and z using said model, but only using the significant fixed effects (the intercept and three way interaction), and plot x, y, z. Does this seem like an alright thing to do in order to communicate what the interaction means assuming I keep the lower order, non significant effects in the model?

Thanks!

Answer 1

If I understand what you are doing, I think it is incorrect; but I'm not sure I understand. First you say

I predict responses of y based on data I generate for y and z using said model, but only using the significant fixed effects

which seems like you used only the significant effects. But then you ask if this is a good way

to communicate what the interaction means assuming I keep the lower order, non significant effects in the model?

I think that whatever is in your model should be in your plot. And statistical significance has nothing to do with it. The predicted values based only on a 3 way interaction without the 2 way or main effects can be very different from those from the full model; and, except in very unusual circumstances, they aren't what you want.

That's why you (correctly) keep the lower order terms in the model