Multimodel Inference

@article{Burnham2004MultimodelI,
  title={Multimodel Inference},
  author={Kenneth P. Burnham and David R. Anderson},
  journal={Sociological Methods \& Research},
  year={2004},
  volume={33},
  pages={261 - 304}
}
The model selection literature has been generally poor at reflecting the deep foundations of the Akaike information criterion (AIC) and at making appropriate comparisons to the Bayesian information criterion (BIC). There is a clear philosophy, a sound criterion based in information theory, and a rigorous statistical foundation for AIC. AIC can be justified as Bayesian using a “savvy” prior on models that is a function of sample size and the number of model parameters. Furthermore, BIC can be… 

Model weights and the foundations of multimodel inference.

TLDR
The usefulness of the weighted BIC (Bayesian information criterion) is suggested as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC.

Bayes Factors and Multimodel Inference

TLDR
Noting the sensitivity of Bayes factors to the choice of priors on parameters, this work defines and proposes nonpreferential priors as offering a reasonable standard for objective multimodel inference.

Using Akaike’s information theoretic criterion in population

Akaike’s information-theoretic criterion for model discrimination (AIC) is often stated to “overfit”, i.e., it selects models with a higher dimension than the dimension of the model that generated

Normalized Information Criteria and Model Selection in the Presence of Missing Data

TLDR
This work proposes a new approach that enables the use of classic well-known information criteria for model selection when there are missing data, and adjusts the current theory of information criteria through normalization, accounting for the different sample sizes used for each candidate model.

An evaluation of prior influence on the predictive ability of Bayesian model averaging

TLDR
It is demonstrated that parsimonious priors may be favorable over priors that favor complexity for making predictions, and BMA performed better than a best single-model approach independently of the prior model weight for 6 out of 16 species.

A Conceptual Introduction to Bayesian Model Averaging

TLDR
In this conceptual introduction, the principles of BMA are explained, its advantages over all-or-none model selection are described, and its utility is showcased in three examples: analysis of covariance, meta-analysis, and network analysis.

Multimodel Inference: Understanding AIC relative variable importance values

The goal of this material is to present extended theory and interpretation for the variable importance weights in multimodel information theoretic (IT) inference. We show that these statistics are a

Selecting Path Models in SEM: A Comparison of Model Selection Criteria

TLDR
A comprehensive evaluation of various model selection criteria, including AIC, BIC, and their extensions, in selecting an optimal path model under a wide range of conditions over different compositions of candidate set, distinct values of misspecified parameters, and diverse sample sizes concludes that the BIC family in general outperformed AIC counterparts unless under small values of omitted parameters and sample sizes, where AIC performed better.

Bayesian Model Averaging as an Alternative to Model Selection for Multilevel Models

TLDR
The Bayesian model averaging technique was investigated as an alternative method to the traditional model selection approaches for multilevel models (MLMs) through the Bayesian and the frequentist frameworks and suggested that BMA was a trustworthy alternative to traditional model comparison and selection approaches.
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