Turning your input variables into ratios of each other

Say you have 3 variables: a,b, c, and d. Instead of using those as inputs, you turn your inputs into ratios of your original variables: a/b, a/c, a/d, b/c, b/d, c/d. In a theoretical sense there is no specific motivation for taking these ratios, but we find (after backward variable selection and 10-fold cross validation and maybe a couple other independent test sets) that we routinely get better predictions when using these ratios compared to when we use the original variables. Is there a name for this? Is this a thing that is done routinely? Is it any different than replacing your input variables with interaction effects? (I guess we're just dividing instead of multiplying) I remember in stats class you're told you have to keep the original variables if you use interaction effects, so it already seems weird to me to only use ratios... Is there some literature I can read about using ratios? It seems like it wouldn't have much validity in terms of a study where the meaning of your variables is important, but if you just want as good a prediction as possible, is there any reason NOT to do this?

/r/statistics Thread