Abstract
Electroencephalography (EEG) studies produce region-referenced functional data in the form of EEG signals recorded across electrodes on the scalp. It is of clinical interest to relate the highly structured EEG data to scalar outcomes such as diagnostic status. In our motivating study, resting-state EEG is collected on both typically developing (TD) children and children with autism spectrum disorder (ASD) aged 2 to 12 years old. The peak alpha frequency (PAF), defined as the location of a prominent peak in the alpha frequency band of the spectral density, is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age. To retain the most amount of information from the data, we consider the oscillations in the spectral density within the alpha band, rather than just the peak location, as a functional predictor of diagnostic status (TD vs ASD), adjusted for chronological age. A covariate-adjusted region-referenced generalized functional linear model is proposed for modeling scalar outcomes from region-referenced functional predictors, which utilizes a tensor basis formed from one-dimensional discrete and continuous bases to estimate functional effects across a discrete regional domain while simultaneously adjusting for additional nonfunctional covariates, such as age. The proposed methodology provides novel insights into differences in neural development of TD and ASD children. The efficacy of the proposed methodology is investigated through extensive simulation studies.