Abstract
Event-related spectral perturbations (ERSPs) capture dynamic changes in electroencephalography (EEG) power across frequency and trial time. Even though they are obtained at the trial level, they are commonly averaged across trials and analyzed at the subject level for enhancing the signal-to-noise ratio. While evoked activity is stimulus-locked, representing the brain's predictable response to stimuli, induced signals that are not strictly locked to stimulus presentation are thought to be generated by higher-order processes, such as attention and integration. Motivated by joint modeling of multilevel (trials nested in subjects) and multivariate (evoked and induced) ERSP data from a visual-evoked potentials (VEP) task, we propose a multilevel multivariate functional principal components analysis (FPCA) for high-dimensional functional outcomes as a function of time and frequency. The proposed estimation procedure utilizes multilevel univariate FPCA decompositions along each variate of the multivariate outcome using fast covariance estimation and incorporates the dependency across outcome variates at each level of the data. Hence, the proposed approach for multilevel multivariate FPCA can efficiently scale up to higher dimensional functional outcomes and increasing number of variates in the multivariate functional outcome vector. Extensive simulations show the efficacy of the proposed approach, while applications to VEP data lead to new insights on autism-specific neural activity patterns. The autistic group shows significantly lower evoked and higher induced gamma power compared to the neurotypical group. In addition, while subject level variation is dominated by variation in the stimulus-locked evoked signal in neurotypical development, it is dominated by induced power in autism.