Suppose I have $m$ competing models. Suppose also that I could classify these models into $s$ sets. For example, I could classify models of migration behavior conditional on climatic conditions by the geographic scope (global vs. local) of the climate measures. Now suppose I fit all of these models and calculate the information criterion. I understand how to find the "best" model. I understand how to compare that model to others and calculate either a relative likelihood (for AIC) or posterior odds (for BIC) based on the IC difference between two models. What I want to do, however, is compare the fit of models in set $s_i$ to models in set $s_{j\neq i}$. How do I do that? What if I want to compare the ICs across all sets (as opposed to two-set comparisons)? Do I need to do some statistical inference here, or, as with the two-model comparisons, can I take the ICs as given?
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asked May 22, 2013 at 22:52
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Using information criterion like AIC and BIC can be applied to compare non-nested models (as well as nested models) and so you should be able to simply compare the AIC's (or BIC's) of the models in set $s_i$ directly against those in set $s_{j:j\neq i}$.