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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?

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    $\begingroup$ This is actually a giant can of worms. e.g. dynamicecology.wordpress.com/2014/10/02/… . I would personally recommend not doing any model simplification unless it's absolutely necessary for model interpretation. $\endgroup$ – Ben Bolker Oct 5 '14 at 21:48
  • $\begingroup$ let me rephrase that slightly (I would insert "data-driven") before "model simplification" $\endgroup$ – Ben Bolker Oct 6 '14 at 0:10
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Model selection is not a simple process unless you are only dealing with a small number of variables. The significance of some variables may depend on others. If you have the time you could try every possible model and pick the 'best' one. There are many criteria for selecting the best model. Refer to any experimental design text book.

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