title: How to avoid mismodelling in GLM-based fMRI data analysis: cross-validated Bayesian model selection.
abstract: Voxel-wise general linear models (GLMs) are a standard approach for analyzing functional magnetic resonance imaging (fMRI) data. An advantage of GLMs is that they are flexible and can be adapted to the requirements of many different data sets. However, the specification of first-level GLMs leaves the researcher with many degrees of freedom which is problematic given recent efforts to ensure robust and reproducible fMRI data analysis. Formal model comparisons that allow a systematic assessment of GLMs are only rarely performed. On the one hand, too simple models may underfit data and leave real effects undiscovered. On the other hand, too complex models might overfit data and also reduce statistical power. Here we present a systematic approach termed cross-validated Bayesian model selection (cvBMS) that allows to decide which GLM best describes a given fMRI data set. Importantly, our approach allows for non-nested model comparison, i.e. comparing more than two models that do not just differ by adding one or more regressors. It also allows for spatially heterogeneous modelling, i.e. using different models for different parts of the brain. We validate our method using simulated data and demonstrate potential applications to empirical data. The increased use of model comparison and model selection should increase the reliability of GLM results and reproducibility of fMRI studies.
authors.affiliation: Bernstein Center for Computational Neuroscience, Berlin, Germany; Department of Psychology, Humboldt-Universität zu Berlin, Germany.
authors.forename: Joram
authors.initials: J
authors.lastname: Soch
authors.affiliation: Bernstein Center for Computational Neuroscience, Berlin, Germany; Berlin Center for Advanced Neuroimaging, Berlin, Germany; Berlin School of Mind and Brain, Berlin, Germany; Excellence Cluster NeuroCure, Charité-Universitätsmedizin Berlin, Germany; Department of Neurology, Charité-Universitätsmedizin Berlin, Germany; Department of Psychology, Humboldt-Universität zu Berlin, Germany.
authors.forename: John-Dylan
authors.initials: JD
authors.lastname: Haynes
authors.affiliation: Bernstein Center for Computational Neuroscience, Berlin, Germany; Berlin Center for Advanced Neuroimaging, Berlin, Germany.
authors.forename: Carsten
authors.initials: C
authors.lastname: Allefeld
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods; D003198:Computer Simulation; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016014:Linear Models; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Bayesian model selection; cross-validation; fMRI-based neuroimaging; mass-univariate GLM; model misspecifcation; underfitting versus overfitting