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I have the following mixed models:

modeloIa<-lmer(log(FstPSAmm2+1)~AntherAreamm2+(1|plant), REML = F)

modeloIIa<-lmer(log(FstPSAmm2+1)~AntherAreamm2*color+(1|plant), REML = F)

modeloIIIa<-lmer(log(FstPSAmm2+1)~AntherAreamm2*color*FlPerBranch+(1|plant), REML = F)

modeloIVa<-lmer(log(FstPSAmm2+1)~color*AntherAreamm2*PlVoldm3+(1|plant), REML = F)

The first one is the null modell. The variable color is the fixed effect I want to test. FlPerBranch and PlVoldm3 are covariables.

How do I select the best model? How do I know if the variables are significant? These two questions are for me a dilemma.

If I use the AIC criterion I should select one model, but if I use the likelihood ratio test, starting from my null modell, I should select another. Any advice will help me a lot, thanks.

Stephan Kolassa
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Andres D
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  • Looking through [our previous questions tagged both "mixed-model" and "model-selection"](https://stats.stackexchange.com/questions/tagged/mixed-model%2bmodel-selection) gives a number of hits. Does anything there help you? – Stephan Kolassa Dec 13 '17 at 16:58
  • See the help file `?lmer` for examples of performing tests with mixed effects models. – AdamO Dec 13 '17 at 17:43

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I would look at mixed effect model selection in Zuur et al. (2009) (? maybe 2007) You could use AICc to aid in model selection for sure but I know he goes into it a lot more in his book. As for the p-values there are two ways I know of. One way would be to install the package lmerTest it gives you pvalues for you model outputs. The other way that I know more about is to use anova (with a chi-square distrib.) in order to get some sort of p-values.

For example if you do an AICc on two models model1 is Y ~ x+(1|y) model2 is Y ~x + z +(1|y) and the aic difference is extremely close you can run an anova on both:

aov(model1,model2, type = "chisq")

and get a p -value telling you the significance of that extra parameter (z)

Leo Ohyama
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