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Cited by 298Functional Brain Connectivity StudiesBayesian Modeling and Causal InferenceStatistical Methods and Inference

The DOI matches its Crossref record; 45 of the 47 references it cites were found in a registry or an index.

Comparing Dynamic Causal Models using AIC, BIC and Free Energy

Open access
Penny, W.D.·2012·NeuroImage
DOI 10.1016/j.neuroimage.2011.07.039PMC PMC3200437
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Abstract

In neuroimaging it is now becoming standard practise to fit multiple models to data and compare them using a model selection criterion. This is especially prevalent in the analysis of brain connectivity. This paper describes a simulation study which compares the relative merits of three model selection criteria (i) Akaike's Information Criterion (AIC), (ii) the Bayesian Information Criterion (BIC) and (iii) the variational Free Energy. Differences in performance are examined in the context of General Linear Models (GLMs) and Dynamic Causal Models (DCMs). We find that the Free Energy has the best model selection ability and recommend it be used for comparison of DCMs.

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Crossref · 10.1016/j.neuroimage.2011.07.039

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Figures

Fig. 1 Design matrix for the full GLM. The nested GLM uses an identical design matrix but with the first three columns removed. The full design matrix comprises N = 351 rows, one for each fMRI scan, and twelve columns, one for each putative experimental effect.
Fig. 1 Design matrix for the full GLM. The nested GLM uses an identical design matrix but with the first three columns removed. The full design matrix comprises N = 351 rows, one for each fMRI scan, and twelve columns, one for each putative experimental effect.CC BY · PubMed Central
Fig. 2 Log Bayes factor of full versus nested model, Log Bf, n, versus the signal to noise ratio, SNR, when the true model is the full GLM for FL (black), AIC (blue) and BIC (red).
Fig. 2 Log Bayes factor of full versus nested model, Log Bf, n, versus the signal to noise ratio, SNR, when the true model is the full GLM for FL (black), AIC (blue) and BIC (red).CC BY · PubMed Central
Fig. 3 Log Bayes factor of nested versus full model, Log Bn, f, versus the signal to noise ratio, SNR, when the true model is the nested GLM for FL (black), AIC (blue) and BIC (red).
Fig. 3 Log Bayes factor of nested versus full model, Log Bn, f, versus the signal to noise ratio, SNR, when the true model is the nested GLM for FL (black), AIC (blue) and BIC (red).CC BY · PubMed Central
Fig. 4 Log Bayes factor of full versus nested model, Log Bf, n, versus the number of data points, N, when the true model is the full GLM for FL (black), AIC (blue), BIC (red) and AICc (green).
Fig. 4 Log Bayes factor of full versus nested model, Log Bf, n, versus the number of data points, N, when the true model is the full GLM for FL (black), AIC (blue), BIC (red) and AICc (green).CC BY · PubMed Central
Fig. 5 Log Bayes factor of nested versus full model, Log Bn, f, versus the number of data points, N, when the true model is the nested GLM for FL (black), AIC (blue), BIC (red) and AICc (green).
Fig. 5 Log Bayes factor of nested versus full model, Log Bn, f, versus the number of data points, N, when the true model is the nested GLM for FL (black), AIC (blue), BIC (red) and AICc (green).CC BY · PubMed Central
Fig. 6 A nested (left) and full (right) DCM. The full DCM is identical to the nested DCM except for having an additional modulatory forward connection from region P to region A. Intrinsic connections are indicated by dotted arrows, modulatory connections by overlaid solid arrows and inputs by solid squares with an arrow.
Fig. 6 A nested (left) and full (right) DCM. The full DCM is identical to the nested DCM except for having an additional modulatory forward connection from region P to region A. Intrinsic connections are indicated by dotted arrows, modulatory connections by overlaid solid arrows and inputs by solid squares with an arrow.CC BY · PubMed Central
Fig. 7 Log Bayes factor of full versus nested model, Log Bf, n, versus the signal to noise ratio, SNR, when the true model is the full DCM for FL (black), AIC (blue) and BIC (red).
Fig. 7 Log Bayes factor of full versus nested model, Log Bf, n, versus the signal to noise ratio, SNR, when the true model is the full DCM for FL (black), AIC (blue) and BIC (red).CC BY · PubMed Central
Fig. 8 Log Bayes factor of nested versus full model, Log Bn, f, versus the signal to noise ratio, SNR, when the true model is the nested DCM for FL (black), AIC (blue) and BIC (red).
Fig. 8 Log Bayes factor of nested versus full model, Log Bn, f, versus the signal to noise ratio, SNR, when the true model is the nested DCM for FL (black), AIC (blue) and BIC (red).CC BY · PubMed Central

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Citations

Cites

Show all 47 references

Research works printed but not linked: 2

  1. Akaike, 1973, Information measures and model selection, Bull. Int. Stat. Inst., 50, 277
  2. Hoeting, 1999, Bayesian model averaging: a tutorial, Stat. Sci., 14, 382

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Related

Metadata

Authors
Penny, W. D.
Affiliations
Wellcome Centre for Human Neuroimaging (GB)
Corresponding author
Penny, W.D.
ORCID
Penny, W.D.
Venue
NeuroImage
Publisher
Elsevier BV
Published
2012-01
Volume
59
Issue
1
Pages
319-330
ISSN
1053-8119 (ISSN-L)
DOI
10.1016/j.neuroimage.2011.07.039
PMC
PMC3200437
OpenAlex
W2150847325
Cited by
298
References
47
Citations by year
2026: 10 · 2025: 21 · 2024: 12 · 2023: 16 · 2022: 20 · 2021: 25 · 2020: 26 · 2019: 19 · 2018: 34 · 2017: 23 · 2016: 29 · 2015: 20 · 2014: 16 · 2013: 18 · 2012: 8
FWCI
6.99
Type
journal article
Language
en
Open access
Licence
Locations
  • NeuroImage (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • UCL Discovery (University College London) (submittedVersion)
  • UEA Digital Repository (University of East Anglia) (submittedVersion)
Funders
Wellcome Trust
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Keywords
dynamic causal modeling, model selection criteria, Akaike information criterion, Bayesian information criterion, variational free energy, brain connectivity, general linear model, model comparison, simulation study
MeSH terms
Bayes Theorem, Brain Mapping, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Models, Neurological, Models, Theoretical, Reproducibility of Results, Linear Models

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