Semiparametric Latent ANOVA Model for Event-Related Potentials

Event-related potentials (ERPs) extracted from electroencephalography (EEG) data in response to stimuli are widely used in psychological and neuroscience experiments. A major goal is to link ERP characteristic components to subject-level covariates. Existing methods typically follow two-step approaches, first identifying ERP components using peak detection methods and then relating them to the covariates. This approach, however, can lead to loss of efficiency due to inaccurate estimates in the initial step, especially considering the low signal-to-noise ratio of EEG data. To address this challenge, we propose a semiparametric latent ANOVA model (SLAM) that unifies inference on ERP components and their association to covariates. SLAM models ERP waveforms via a structured Gaussian process prior that encodes ERP latency in its derivative and links the subject-level latencies to covariates using a latent ANOVA. This unified Bayesian framework provides estimation at both population- and subject- levels, improving the efficiency of the inference by leveraging information across subjects. We automate posterior inference and hyperparameter tuning using a Monte Carlo expectation-maximization algorithm. We demonstrate the advantages of SLAM over competing methods via simulations. Our method allows us to examine how factors or covariates affect the magnitude and/or latency of ERP components, which in turn reflect cognitive, psychological or neural processes. We exemplify this via an application to data from an ERP experiment on speech recognition, where we assess the effect of age on two components of interest. Our results verify the scientific findings that older people take a longer reaction time to respond to external stimuli because of the delay in perception and brain processes.