I am a bachelor student in biology and for a project work, I have a model with a design like this (A, B & C are fixed factors, D is random and nested in C):
lmer1 = lmer(y~A+B+C+A:B+A:C+B:C+A:B:C+(1+A+B|D:C)) summary(lmer1)
If A:B:C is not significant, I can simplify the model by removing this term:
lmer2 = lmer(y~A+B+C+A:B+A:C+B:C+(1+A+B|D:C)) anova (lmer1,lmer2) summary(lmer2)
If now the p value from the ANOVA table >0.05, I can proceed with lmer2. But here is my question: how should I simplify further if there are still unsignificant fixed and random terms? Should the next step be removing A:B (or A:C or B:C) from the fixed part or removing from the random part of the model?