I am curious, is there a way to optimize a regression according to a specific statistic?
Let's say I am interested in a model with the best possible AIC statistic (or MSE or whatever measurement I am interested in) - could I somehow direct the regression to give me the top X models that would do this? (Of course I would not ignore the other measures, but would it be possible to ask for this?) What software supports this, or would you write your own code (in say R)?
Also in general, when multiple regression results are displayed (let's say an all-possible or best-subset regression is done), is there a ranking and if so, according to what measure/criteria?
I'm not saying that this is the best way to evaluate models, but perhaps it would be a way to explore candidate models? (This is really not my main question though.)
Thanks .. learning a lot reading this site.