Proper and improper use of AIC

Ecologists are increasingly applying Akiake’s Information Criterion (AIC) to the problems of model selection and multi-model inference.  Model selection frequently consists of keeping all models with AIC differences within a threshold of the minimum calculated, and then using these differences to construct model weights.  Often model weights are then used to improve parameter estimates.  In fact, surprisingly little is known regarding the reliability of such approaches.  Using very simple examples I illustrate what I call the model weight paradox, which is when models having high weight in fact have poor parameter estimates and are less parsimonious than simpler models.  I also address the problem of how to interpret model weights and illustrate how the paradox affects the reliability of weighted parameter estimates and the predictive ability of weighted models.