# Comparing mixed effects models

I have 2 dependent variables and 1 explanatory variable of interest (there will be other control variables). I have a data structure requiring crossed random effects, so will be running a mixed effects model.

I am testing whether the explanatory variable of interest explains dependent variable 1 or 2 better. I was planning to do two separate models (for each dependent variable) and then comparing results. What should I compare to answer this question? Statistical significance? Size of coefficient? Fit statistics like AIC? Any help much appreciated.

Model:

$$Y_{ijkl} = x′_{ijkl}\beta + \nu_i + \nu_j + \nu_k + \epsilon_{ijkl}$$

where

• $$\nu_i$$ = random intercept for variable $$i$$
• $$\nu_j$$ = random intercept for variable $$j$$
• $$\nu_k$$ = random intercept for variable $$k$$
• $$\epsilon_{ijkl}$$ = random error term
• It might help to write out your model's equations. I'm having a little trouble understanding what you mean by "crossed random effects," especially with only one explanatory variable. – Ben Ogorek Nov 17 '18 at 22:00
• Thank you very much. I added the model. Also, I should have said that there are potentially other control variables in the model, but there is 1 explanatory variable of interest that I am testing to see whether it "explains" dependent variable 1 or 2 better. – Marissa Nov 21 '18 at 16:47
• Hi, just wanted to see if anyone had any thoughts/comments on this? – Marissa Nov 26 '18 at 22:57