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Modeling Region-Referenced Longitudinal Functional Electroencephalography Data


Highly structured data collected in a variety of biomedical applications such as electroencephalography (EEG) are discrete samples of a smooth functional process observed across both temporal and spatial dimensions. EEG data is conceptualized as region-referenced longitudinal functional data in which the functional dimension captures local signal dynamics, the longitudinal dimension tracks changes over the course of an experiment, and the regional dimension indexes spatial information across electrodes on the scalp. This complex data structure exhibits intricate dependencies with rich information but its dimensionality and size produce significant obstacles for interpretation, estimation, and inference. Motivated by a series of EEG studies in children with autism spectrum disorder (ASD), a set of computationally efficient methods for these high-dimensional data structures are proposed that both maintain information along each dimension and yield interpretable components and inferences.

The first half of the work considers decompositions of the total variation. To begin, a multi-dimensional functional principal components analysis (MD-FPCA) is introduced which decomposes the total variation into subject- and electrode-level components and for each level employs a two-stage functional principal components decomposition sequentially across functional and longitudinal time. Next, a hybrid principal components analysis (HPCA) for region-referenced longitudinal functional EEG data is proposed which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The second half of the work shifts to modeling associations and introduces a covariate-adjusted region-referenced generalized functional linear model (CARR-GFLM) for modeling scalar outcomes from region-referenced functional predictors. CARR-GFLM 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 non-functional covariates, such as age. Proposed methods not only help identify neurodevelopmental differences between typically developing and ASD children but can also be used to study the heterogeneity within children with ASD. The performance of all proposed methods is studied via extensive simulations.

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