Mixed models: if the interaction is significant but the main effect is not, should I remove the factor from the fixed effects or the random slope? I run a glmer model using two factors both as fixed effects and as random slopes. Here is the formula:
maximal_RTs.model = glmer(RTs ~ FT1* FT2+ (1+ FT1* FT2|Num_part)
                          , data = data_RTs_hands
                          , family=inverse.gaussian(link="identity")
                          , control=glmerControl(optimizer="bobyqa"
                                                 , optCtrl=list(maxfun=1e6))
)

The model converges and the summary() functions show that the main effect of FT2 is significant and the interaction is significant, but the simple effect of FT1 is not significant.
Should I reduce the model by removing FT1? And if yes, should I remove it from the fixed effects or the random slopes?
Thank you,
 A: The usually rule of thumb is if the interaction is significant, you retain all lower-order effects that are components of it.
The interaction term is telling you the effect of FT1 depends on the level of FT2, and the effect of FT2 depends on the level of FT1. Ergo, FT1 is significant by proxy, and funnels into the equation that is used to determine the value of your response for a given set of predictor values.
As for the random slopes, that is difficult to say as it is unclear what your experimental design is. There are two schools of thought, generally, around the retention of random effects. 1) If you designed your experiment to include random effects, then you should keep them in your model, regardless of significance, as there is usually a small cost to doing so. 2) If you are short on degrees of freedom then removing non-significant random effects can be justifiable, but that does not meaning removing the fixed effect necessarily! The significance of a fixed effect term in your model does not necessarily mean that your random effect is non-significant even if the former is part of the RE's definition. The piece that goes before the "|" is simply telling the model how the experiment was structured - here is a good explanation of that.
Let me know if anything was unclear.
