I wonder whether it is sensible to use the following method of assessing relative importance of variables in a model.
- Compute a model and its $AIC$. Let's say it has $k$ predictors.
- Compute $k$ submodels, each of which has one predictor removed. Compute $AIC$ for all the submodels.
- Compute $k$ times $\Delta AIC$, which is defined as $AIC_{submodel} - AIC_{full~model}$.
- And then the relative importance of each variable is being quantified by the magnitude of its corresponding $\Delta AIC$.
EDIT. Just to clarify a few things: this approach is meant to be used in a specific situation, when one has a bunch of otherwise equally important predictors (that is, none of them is considered more important than others a priori) and want to figure out which of the predictors has the strongest relationship with the outcome. The idea is that the difference in AIC quantifies relative likelihood that one model minimizes information loss and not the other, so having $\Delta AIC$ defined for all predictors one can judge which of them minimize information loss the most.
So the aim here is to establish a relative hierarchy of predictors within a single model. Does this strategy make any sense?