Model weights and the foundations of multimodel inference.

Area of Science:

• Ecology
• Wildlife Biology
• Statistical Modeling

Background:

• Akaike's Information Criterion (AIC) is widely used in wildlife biology and ecology for model selection and averaging.
• AIC implicitly favors complex models through its default prior model weights.
• The Bayesian paradigm provides a more comprehensive framework for multimodel inference.

Purpose of the Study:

• To advocate for the Bayesian paradigm as a broader framework for multimodel inference in ecology.
• To evaluate the performance of AIC-based tools within the Bayesian framework.
• To propose the weighted Bayesian Information Criterion (BIC) as a computationally simpler alternative to AIC.

Main Methods:

• Comparison of AIC and Bayesian approaches for model selection and averaging.
• Implicit prior model weights in AIC were analyzed.
• Weighted BIC was suggested as an alternative to AIC.
• Bayes factors were discussed, including technical challenges and solutions.
• A logistic regression model was used for illustration.

Main Results:

• AIC's implicit priors strongly favor complex models, potentially ignoring simpler ones.
• Weighted BIC offers a computationally simple alternative based on explicit prior model probabilities.
• Both AIC and weighted BIC are approximations to exact Bayes factors.
• AIC weighting demonstrates a predisposition to favor complex models.

Conclusions:

• The Bayesian paradigm offers a more integrated approach to model selection and averaging in ecological studies.
• Explicitly setting prior model probabilities, as with weighted BIC, is preferable to AIC's default priors.
• Caution is advised when using BIC for approximate posterior model weights due to AIC's complex model bias.
• Further research into practical Bayes factor computation is warranted.