  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.
