# 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
, 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,

• Don't trust "significance" tests of "main effects" for predictors involved in interactions. They test whether the "main effect" coefficient is different from 0 when all of the interacting predictors are at 0 or at reference levels. Simply re-centering the F2 predictor can lead to an apparent change in the "significance" of the F1 "main effect." See this page.
– EdM
Feb 2 at 20:50

• Thank you for your response, that was very clear! I created the model following Barr, 2013 "maximal random structure allowed by the design" and given that the model converged and the anova() function showed that the BIC was lower compared to reduced models, I decided to use it. F1 has 3 levels/condition and represent my primary research question, while F2 represents the sequence of trials that were randomly generated (Sequence effects, show that the response changes depending on the type of the previous trial, e.g. incongruent or congruent). I am not sure about the random slopes thought..