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I am running a glmm with three fixed effects:

opponent 1 size ("1")
opponent 2 size ("2")
opponent 1 size - opponent 2 size ("diff")

I am unable to run all three variables in the model at once because of the "diff" variable being correlated with the "1" and "2" variables. How, then, do I decide which is the best model, when all the different combinations I can test are not nested within one another? Or can I consider the first two variables to be nested within the third one, since they are both used to calculate "diff"? I have these combinations of variables and their corresponding AICs (variable(s) followed by AIC in parentheses):

variable(s) (AIC):
diff (223)
1 (231)
2 (262)
1,2 (265)
1,diff (265)
2,diff (265)

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Run the model with the first two predictors. It is not necessary to include the third, since this is merely a linear combination of the first two.

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  • $\begingroup$ But the predictive power of the third variable is the one I (and my reviewers) are most interested in! :) $\endgroup$ Sep 10, 2014 at 18:58
  • $\begingroup$ Can you leave one of the first predictors out, then? $\endgroup$
    – coanil
    Sep 10, 2014 at 20:28
  • $\begingroup$ No, unfortunately not. The goal is to determine which of those three factors best explains the outcome of a contest. $\endgroup$ Sep 10, 2014 at 20:35

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