Multi-model inference through projections in model space

TL;DR

This paper introduces a novel multi-model inference method using projections in model space, enabling more accurate estimation of the true model and its divergence from the generating process, surpassing traditional information criterion approaches.

Contribution

It extends Akaike's work by incorporating divergence relationships among models to construct a model space that estimates the generating process more reliably.

Findings

Constructed a model space including an estimated location for the generating process.

Demonstrated that properties estimated from projections are more accurate than model averaging.

Applicable across scientific fields using information criteria for model selection.

Abstract

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.