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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
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  • $\begingroup$ 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. $\endgroup$ – Ben Ogorek Nov 17 '18 at 22:00
  • $\begingroup$ 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. $\endgroup$ – Marissa Nov 21 '18 at 16:47
  • $\begingroup$ Hi, just wanted to see if anyone had any thoughts/comments on this? $\endgroup$ – Marissa Nov 26 '18 at 22:57

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