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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,

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    $\begingroup$ 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. $\endgroup$
    – EdM
    Commented Feb 2, 2022 at 20:50

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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.

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    $\begingroup$ 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.. $\endgroup$
    – TomC
    Commented Feb 4, 2022 at 10:38
  • $\begingroup$ If F2 is just a representation of the structure of your experimental design then you don't need to include it in your fixed effects - fixed effects (IMO) are just for the hypotheses that you are actually interested in testing! However, if you were actually interested in how F2 affects F1 then you might keep it in your fixed effects. By putting it as a RE you are essentially accounting for it's influence and separating this out from the effect of F1. $\endgroup$
    – André.B
    Commented Feb 22, 2022 at 21:42

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