Bootstrapping fMRI Data: Dealing with Misspecification

The validity of inference based on the General Linear Model (GLM) for the analysis of functional magnetic resonance imaging (fMRI) time series has recently been questioned. Bootstrap procedures that partially avoid modeling assumptions may offer a welcome solution. We empirically compare two voxelwise GLM-based bootstrap approaches: a semi-parametric approach, relying solely on a model for the expected signal; and a fully parametric bootstrap approach, requiring an additional parameterization of the temporal structure. While the fully parametric approach assumes independent whitened residuals, the semi-parametric approach relies on independent blocks of residuals. The evaluation is based on inferential properties and the potential to reproduce important data characteristics. Different noise structures and data-generating mechanisms for the signal are simulated. When the model for the noise and expected signal is correct, we find that the fully parametric approach works well, with respect to both inference and reproduction of data characteristics. However, in the presence of misspecification, the fully parametric approach can be improved with additional blocking. The semi-parametric approach performs worse than the (fully) parametric approach with respect to inference but achieves comparable results as the parametric approach with additional blocking with respect to image reproducibility. We demonstrate that when the expected signal is incorrect GLM-based bootstrapping can overcome the poor performance of classical (non-bootstrap) parametric inference. We illustrate both approaches on a study exploring the neural representation of object representation in the visual pathway.