A bit of a newbie statistics question. In a GLM, would it be sound to use a dependent variable that incorporates one (or more) independent variables? For example, if my dependent variable is number-of-occurences-per-sq-km of a site ("density"), could I use site area (measured in sq km) as one of my independent variables? My intuition says that's a bad idea, but I'm not sure if that's the case.
I do not know the exact problem you are looking to solve. But If I was to extrapolate from what you are suggesting, we can look at something like number of fire stations in a city.
It would absolutely matter how big the city is area wise to look at the trends, and once again its a subjective call based on the problem you are solving and the other variables involved, in my case it could the number of chemical industries around, fuel depots and so on.
So contrary to your intuition might not be a bad idea after all.
Hope my perspective helps!