The GLM-Spectrum: A multilevel framework for spectrum analysis with covariate and confound modelling

Abstract The frequency spectrum is a central method for representing the dynamics within electrophysiological data. Some widely used spectrum estimators make use of averaging across time segments to reduce noise in the final spectrum. The core of this approach has not changed substantially since the 1960s, though many advances in the field of regression modelling and statistics have been made during this time. Here, we propose a new approach, the General Linear Model (GLM) Spectrum, which reframes time averaged spectral estimation as multiple regression. This brings several benefits, including the ability to do confound modelling, hierarchical modelling and significance testing via non-parametric statistics. We apply the approach to a dataset of EEG recordings of participants who alternate between eyes-open and eyes-closed resting state. The GLM-Spectrum can model both conditions, quantify their differences, and perform denoising through confound regression in a single step. This application is scaled up from a single channel to a whole head recording and, finally, applied to quantify age differences across a large group-level dataset. We show that the GLM-Spectrum lends itself to rigorous modelling of within- and between-subject contrasts as well as their interactions, and that the use of model-projected spectra provides an intuitive visualisation. The GLM-Spectrum is a flexible framework for robust multi-level analysis of power spectra, with adaptive covariance and confound modelling.