EEG experiments yield high-dimensional event-related potential (ERP) data in response to repeatedly presented stimuli throughout the experiment. Changes in the high-dimensional ERP signal throughout the duration of an experiment (longitudinally) is the main quantity of interest in learning paradigms, where they represent the learning dynamics. Typical analysis, which can be performed in the time or the frequency domain, average the ERP waveform across all trials, leading to the loss of the potentially valuable longitudinal information in the data. Longitudinal time-frequency transformation of ERP (LTFT-ERP) is proposed to retain information from both the time and frequency domains, offering distinct but complementary information on the underlying cognitive processes evoked, while still retaining the longitudinal dynamics in the ERP waveforms. LTFT-ERP begins by time-frequency transformations of the ERP data, collected across subjects, electrodes, conditions and trials throughout the duration of the experiment, followed by a data driven multidimensional principal components analysis (PCA) approach for dimension reduction. Following projection of the data onto leading directions of variation in the time and frequency domains, longitudinal learning dynamics are modeled within a mixed effects modeling framework. Applications to a learning paradigm in autism depict distinct learning patterns throughout the experiment among children diagnosed with Autism Spectrum Disorder and their typically developing peers. LTFT-ERP time-frequency joint transformations are shown to bring an additional level of specificity to interpretations of the longitudinal learning patterns related to underlying cognitive processes, which is lacking in single domain analysis (in the time or the frequency domain only). Simulation studies show the efficacy of the proposed methodology.
Keywords: Event-related potentials; Longitudinal functional data analysis; Mixed effects models; Multidimensional PCA; Wavelets.