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In the current literature, people are predicting X. I would like to show that the current models are more suited to predict Y than X.

I have two equivalent models for the two different criteria. They will be linear mixed models, but for simplicity, let's assume:

M1: X = A + B + C

M2: Y = A + B + C

How would I test which variable is better predicted by the model? I was thinking of comparing R² between both models. Would this be correct? Is there a way to test whether the difference in R² is significant?

I understand that I could include a dummy variable indicating whether to predict X or Y. This would allow me to tell whether there is a difference between both models. However, I would like to make a statement about the difference of goodness of fit between both models.

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Are you saying that you have 5 columns in a dataset: A, B, C, X and Y, you've made two models and want to know which model has a better fit? If so, the way to determine that completely depends on what you care about. Assuming you care only about minimising residuals, you may like to simply compare SSE. You may also like to normalise X and Y first to make a fairer comparison.

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  • $\begingroup$ Yes, I would scale all variables. That would make for a better comparison, right? Is there a way to check if SSE differs significantly? Put differently: How could I test whether any differences in SSE are meaningful? $\endgroup$
    – Max J.
    Nov 9, 2020 at 10:37
  • $\begingroup$ Would you be able to provide more context as to why you want to do this. It is a very strange thing to do and you might end up be better off predicting A, B and C from X and Y depending on the context $\endgroup$ Nov 9, 2020 at 10:39
  • $\begingroup$ Context added in the question. $\endgroup$
    – Max J.
    Nov 11, 2020 at 12:31

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