Modeling Time-varying Trends in ERP Data with Applications to an Implicit Learning Paradigm in Autism

Event-related potential (ERP) studies are a subset of experimental frameworks within the field of electroencephalography (EEG) that focus on ERPs, the electrical potential outputted by a subject's brain when presented with an implicit task in the form of stimuli. Data comprise an ERP repetition observed for each stimulus across electrodes on the scalp, producing a complex data structure consisting of a functional, longitudinal and spatial dimension. In typical ERP studies, the dimension of data is reduced into a single measure for each subject by cross-sectionally averaging ERP across longitudinal and spatial repetitions. Features are then extracted from the averaged ERP and analyzed using simple statistical methods, ignoring additional information that may be found in the collapsed dimensions. In this dissertation, three types of methodology are proposed for preserving and analyzing the lost dimensions of ERP data. The first method, moving average processed ERP (MAP-ERP), is a two-step approach comprised of a meta-preprocessing step to preserve longitudinal information and a weighted mixed effects regression framework to allow modeling of the resulting meta-preprocessed data. The proposed robust functional clustering (RFC) algorithm identifies substructures in features of the longitudinal ERP processes while accounting for subject-level covariance heterogeneity induced by meta-preprocessing. Finally, the proposed multidimensional functional principal components analysis (MD-FPCA) utilizes a two-stage procedure to summarize important characteristics across all three dimensions of the ERP data structure into an interpretable, low-dimensional form. Proposed methods are applied to a study on neural correlates of visual implicit learning in young children with autism spectrum disorder (ASD). Applications of the proposed methods reveal meaningful trends and substructures in the implicit learning processes of ASD children when compared to typically developing controls. Results indicate proposed methodology effectively preserves important information contained within the multiple dimensions of ERP