Linear mixed model comparison with ANOVA R

Question

I have two models:

model1 = y~ a+b*c+ 1|d

model2 = y~ a*e+c+1|d

I wanted to compare how they do.

anova(model1, model2)

This is the result:

Why is the p value 0?

Thank you!

Desperate grad student

Answer 1

Hi Desperate Grad student! Typically, the ANOVA test is used to test the necessity of a complex model with respect to a simpler, more parsimonious model. Since, in your case, you're comparing two models with the same number of parameters, you have 0 degrees of freedom (where df = # of parameters in the complex model - # of parameters in the simpler model). This is why you have an absent p-value associated with this comparison.

However, since you have the information criteria for both of these models (AIC/BIC), you can use that to compare the two. Here, model 1 is favorable since its AIC and BIC are lower than the IC for model 2.

If you're set on using the ANOVA approach to compare models, consider creating an "intercept only" model using model0 <- y ~ 1 as your basis for comparison.