Multilevel hybrid principal components analysis for region‐referenced functional electroencephalography data

Abstract

Electroencephalography experiments produce region-referenced functional data representing brain signals in the time or the frequency domain collected across the scalp. The data typically also have a multilevel structure with high-dimensional observations collected across multiple experimental conditions or visits. Common analysis approaches reduce the data complexity by collapsing the functional and regional dimensions, where event-related potential (ERP) features or band power are targeted in a pre-specified scalp region.This practice can fail to portray more comprehensive differences in the entire ERP signal or the power spectral density (PSD) across the scalp. Building on the weak separability of the high-dimensional covariance process, the proposed multilevel hybrid principal components analysis (M-HPCA) utilizes dimension reduction tools from both vector and functional principal components analysis to decompose the total variation into between-and within-subject variance. The resulting model components are estimated in a mixed effects modeling framework via a computationally efficient minorization-maximization algorithm coupled with bootstrap. The diverse array of applications of M-HPCA is showcased

Central Posterior Envelopes for Bayesian Functional Principal Component Analysis

“…as longitudinally observed functional data) and be part of analysis rather than collapsed via averaging. FPCA modeling has been considered for high-dimensional functional data, especially in EEG data applications involving a spatial or a longitudinal dimension (Shamshoian et al, 2022;Li et al, 2020;Campos et al, 2022;Scheffler et al, 2019Scheffler et al, , 2020Hasenstab et al, 2017). Developments rely on simplifying assumptions on the higher dimensional covariance via strong or weak separability.…”

“…A major tool for dimension reduction is the functional principal component analysis (FPCA) for modeling functional variability in the data in lower dimensions (Wang et al, 2016;Yao et al, 2012;Cardot, 2007). Recent literature on FPCA models complex dependencies among the functional observations that are observed in close proximity with respect to time or space (Chen and Müller, 2012;Greven et al, 2010;Crainiceanu et al, 2009;Di et al, 2009;Hasenstab et al, 2017;Scheffler et al, 2020;Campos et al, 2022;Zipunnikov et al, 2011;Baladandayuthapani et al, 2008;Staicu et al, 2010). Bayesian FPCA (BFPCA) offers uncertainty quantification on the functional model components, including the mean and eigenfunctions, via credible intervals, without the need for bootstrap.…”