Functional-Coefficient Models for Multivariate Time Series in Designed Experiments: with Applications to Brain Signals

TL;DR

This paper introduces a flexible, non-linear mixed-effects model for analyzing multivariate time series in designed experiments, specifically applied to EEG data to uncover brain connectivity differences in ADHD.

Contribution

The paper proposes the MXFAR model and the fPDC measure, enabling non-linear, subject-specific, and group-difference analysis of brain signals in EEG studies.

Findings

Identified altered brain networks in ADHD patients.

Demonstrated the model's robustness to model mis-specification.

Showed the framework's ability to incorporate various covariates.

Abstract

To study the neurophysiological basis of attention deficit hyperactivity disorder (ADHD), clinicians use electroencephalography (EEG) which record neuronal electrical activity on the cortex. Instead of focusing on single-channel spectral power, a novel framework for investigating interactions (dependence) between channels in the entire network is proposed. Although dependence measures such as coherence and partial directed coherence (PDC) are well explored in studying brain connectivity, these measures only capture linear dependence. Moreover, in designed clinical experiments, these dependence measures are observed to vary across subjects even within a homogeneous group. To address these limitations, we propose the mixed-effects functional-coefficient autoregressive (MXFAR) model which captures between-subject variation by incorporating subject-specific random effects. The advantages of the MXFAR model are the following: (i) it captures potential non-linear dependence between channels; (ii) it is nonparametric and hence flexible and robust to model mis-specification; (iii) it can capture differences between groups when they exist; (iv) it accounts for variation across subjects; (v) the framework easily incorporates well-known inference methods from mixed-effects models; (vi) it can be generalized to accommodate various covariates and factors. Then, we formulate a novel non-linear spectral measure, the functional partial directed coherence (fPDC), to extract dynamic cross-dependence patterns at different frequency oscillations. Finally, we apply the proposed MXFAR-fPDC framework to analyze multichannel EEG signals and report novel findings on altered brain functional networks in ADHD patients.