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

Spectrum estimators that make use of averaging across time segments are ubiquitous across neuroscience. 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 first-level EEG resting-state dataset alternating 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.