Spatio-Spectral Mixed Effects Model for Functional Magnetic Resonance Imaging Data.

The goal of this paper is to model cognitive control related activation among predefined regions of interest (ROIs) of the human brain while properly adjusting for the underlying spatio-temporal correlations. Standard approaches to fMRI analysis do not simultaneously take into account both the spatial and temporal correlations that are prevalent in fMRI data. This is primarily due to the computational complexity of estimating the spatio-temporal covariance matrix. More specifically, they do not take into account multi-scale spatial correlation (between-ROIs and within-ROI). To address these limitations, we propose a spatio-spectral mixed effects model. Working in the spectral domain simplifies the temporal covariance structure because the Fourier coefficients are approximately uncorrelated across frequencies. Additionally, by incorporating voxel-specific and ROI-specific random effects, the model is able to capture the multi-scale spatial covariance structure: distance-dependent local correlation (within an ROI), and distance-independent global correlation (between-ROIs). Building on existing theory on linear mixed effects models to conduct estimation and inference, we applied our model to fMRI data to study activation in pre-specified ROIs in the prefontal cortex and estimate the correlation structure in the network. Simulation studies demonstrate that ignoring the multi-scale correlation leads to higher false positives.