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

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Comparing Dynamic Causal Models using AIC, BIC and Free Energy

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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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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).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).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).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).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.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).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).CC BY · PubMed Central

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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: hybrid
doi.org
Licence: cc-by
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
creativecommons.org/licenses/by/3.0/ (vor, 562 d)
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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Comparing Dynamic Causal Models using AIC, BIC and Free Energy

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