This may be an obvious question: what do you do when the AIC or BIC choose a model that makes no sense in reality.
I'm looking at data for predictors of hospital selection, and things like a spouse's age are on the right-hand side of the lowest-BIC regression, whereas more obvious things like wealth and education are not.
The BIC of the "best-fit" model is significantly different from the BIC of a more "logical" model, using Rafferty (1995)'s criteria for strength of evidence.
So, my basic question is: do I blindly follow the BIC or do I add in things that I think should be in the equation, even though they'll raise the BIC?
EDITED TO ADD: the difference in the BICs of the "best fit" vs "logical" models is 14 in favor of the best-fit model. The difference in the AICs, however, is 2, in favor of the "logical" model