# Comparing functional hypotheses accounting for uncertain interpretation of their predictions

I am interested in using an information-theoretic approach (likely AIC) to compare the explanatory power of several functional hypotheses. As an example, hypothesis H1 predicts significant association between the dependent variable X and one or more of the variables A, B, C, while hypothesis H2 predicts significant associations between X and one or both of the variables E, F.

Though I may anticipate that D and E correlate with X under H2, due to a lack of prior work on the system this is not certain. This is to say, finding that D is significantly associated with X and that E is not, or vice versa, should not be seen as weaker support for H2 than if both variables were significantly associated with X. Said a third way, I don’t know if it’s appropriate to potentially penalize a model for my imprecise interpretation of its predictions.

Given this is, it best to:

(1) formulate each hypothesis as a full model, i.e. H1=X~A+B+C and H2=X~E+F or

(2) formulate each hypothesis as every possible sub-set of associated variables, i.e. H11=X~A+B+C, H12=X~A+B, H13=X~A+C ... H1k=X~A or perhaps

(3) perform feature selection on each hypothesis to determine the best set of variables to characterize that hypothesis?