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 with two studies of individuals with autism. While ERP responses to match vs mismatch conditions are compared in an audio odd-ball paradigm in the first study, short-term reliability of the PSD across visits is compared in the second. Finite sample properties of the proposed methodology are studied in extensive simulations.

Keywords: autism spectrum disorder (ASD); electroencephalography (EEG); functional data analysis; marginal covariance; multilevel functional principal components analysis.

FIGURE 1

(a) In the audio odd-ball paradigm, the image appears for the full 2000ms and a spoken word is heard 1000ms after the onset of the image. The functional observation to be considered is time-locked to the onset of the audio, creating an ERP that is from −100ms to 1000ms. (b) The ERP waveform displaying the characteristic components P200 and N400. (c) In the ABC-CT feasibility study, PSD are recorded on two visits, approximately a week apart. (d) The estimated mean relative μ(t) as a function of frequency in Hz.

FIGURE 2

(a) The estimated overall mean function μ(t) in the audio odd-ball paradigm. (b) Positions of the 6 electrodes used in the analysis of the audio odd-ball paradigm highlighted. (c) Positions of the 18 electrodes used in the analysis of the ABC-CT feasibility study data highlighted.

FIGURE 3

The estimated leading participant-level eigenvectors $v_{d1}^{(1)}(r)$ (given in (a)) and condition-level eigenvector $v_{d1}^{(2)}$ (given in (b)) represent a contrast between electrodes from the anterior and posterior regions of the scalp for all groups. The estimated leading two eigenfunctions for the participant-level variation ${\varphi }_{d\ell }^{(1)}$ (middle row) and condition-level variation ${\varphi }_{dm}^{(2)}$ (bottom row) for each diagnostic group.

FIGURE 4

The estimated group, region and condition-specific mean functions η_dj(r, t) in the audio odd-ball paradigm.

FIGURE 5

The estimated leading (a) participant-level eigenvector $v_{d1}^{(1)}(r)$ and (b) day-level eigenvector $v_{d1}^{(2)}$. The estimated leading two eigenfunctions for the participant-level variation ${\varphi }_{d\ell }^{(1)}$ (middle row) and day-level variation ${\varphi }_{dm}^{(2)}$ (bottom row) for each diagnostic group.