Covariate-adjusted hybrid principal components analysis for region-referenced functional EEG data.

Electroencephalography (EEG) studies produce region-referenced functional data via EEG signals recorded across scalp electrodes. The high-dimensional data can be used to contrast neurodevelopmental trajectories between diagnostic groups, for example between typically developing (TD) children and children with autism spectrum disorder (ASD). Valid inference requires characterization of the complex EEG dependency structure as well as covariate-dependent heteroscedasticity, such as changes in variation over developmental age. In our motivating study, EEG data is collected on TD and ASD children aged two to twelve years old. The peak alpha frequency, a prominent peak in the alpha spectrum, is a biomarker linked to neurodevelopment that shifts as children age. To retain information, we model patterns of alpha spectral variation, rather than just the peak location, regionally across the scalp and chronologically across development. We propose a covariate-adjusted hybrid principal components analysis (CA-HPCA) for EEG data, which utilizes both vector and functional principal components analysis while simultaneously adjusting for covariate-dependent heteroscedasticity. CA-HPCA assumes the covariance process is weakly separable conditional on observed covariates, allowing for covariate-adjustments to be made on the marginal covariances rather than the full covariance leading to stable and computationally efficient estimation. The proposed methodology provides novel insights into neurodevelopmental differences between TD and ASD children.