  Information criteria have had a profound impact on modern ecological science.
They allow researchers to estimate which probabilistic approximating models are
closest to the generating process. Unfortunately, information criterion
comparison does not tell how good the best model is. Nor do practitioners
routinely test the reliability (e.g. error rates) of information
criterion-based model selection. In this work, we show that these two
shortcomings can be resolved by extending a key observation from Hirotugu
Akaike's original work. Standard information criterion analysis considers only
the divergences of each model from the generating process. It is ignored that
there are also estimable divergence relationships amongst all of the
approximating models. We then show that using both sets of divergences, a model
space can be constructed that includes an estimated location for the generating
process. Thus, not only can an analyst determine which model is closest to the
generating process, she/he can also determine how close to the generating
process the best approximating model is. Properties of the generating process
estimated from these projections are more accurate than those estimated by
model averaging. The applications of our findings extend to all areas of
science where model selection through information criteria is done.
