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model specification in lmer

Hello all

I am attempting to fit a mixed model in lmer. I have an experimental design
with families nested within populations in two different treatments, and I
want to test the effects of Pop, Trt, and Pop:Trt as fixed factors, and
Family and Family*Trt as random factors.

 

My full model would be:

model1=lmer(Trait~Pop*Trt + (Trt|Family)

I can then use:

model2=lmer(Trait~Pop*Trt + (1|Family)

and

anova(model1, model2) would provide signification for the interaction term.

 

I would need a third model with only the interaction term, so that I can
compare it to the full model and obtain significance for the family term.
But I can't figure out how to do this last part.

 

Can I just compare model2 to a model with no random part?

 

Thank you so much for your help in advance.