Model Weights and the Foundations of Multimodel Inference

Abstract

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Effective Culvert Placement and Design to Facilitate Passage of Amphibians across Roads

“…BIC tends to favor simpler models than AIC whenever n > 8 , Link and Barker 2006. BIC assigns uniform prior probabilities across all models (i.e., equal 1/R), whereas in AIC and AICc, prior probabilities increase with sample size Anderson 2004, Link andBarker 2010).…”

“…Some authors argue that BIC requires the true model to be included in the model set, whereas AIC or AICc does not . However, Link andBarker (2006, 2010) ##set up named list names(Cand.set) <-c("logit", "probit", "cloglog") ##compare models ##model names will be taken from the list if modnames is not specified bictab(cand.set = Cand.set) ## End(Not run)…”

Temporal Variation in the Carrying Capacity of a Perennial Grass Population

“…We recognize that readers may prefer to compare models using other approaches (Burnham and Anderson 2004;Richards 2005;Stephens et al 2005;Link and Barker 2006). For these readers, appendix B provides (a) values of the Bayes Information Criterion (BIC), BIC weights, and Bayes factors (Link and Barker 2006) and (b) a significance test of the null hypothesis that K is constant.…”

“…For these readers, appendix B provides (a) values of the Bayes Information Criterion (BIC), BIC weights, and Bayes factors (Link and Barker 2006) and (b) a significance test of the null hypothesis that K is constant. Uncorrected and corrected AIC values are also provided in appendix B.…”

State‐level variation in conservation investment by a major nongovernmental organization

“…The model with the smallest Akaike Information Criteria (AIC) value was considered the most parsimonious model. Following standard procedures, we calculated model weights, which indicate the probability that the model is true given that truth is in the model set (Link & Barker 2006). Following Johnson & Omland (2004), we then constructed the 95% confidence set of models, that is, the smallest number of models whose cumulative weights summed to 0.95.…”