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.

翻译：从脑电图数据中提取的事件相关电位（ERP）响应于刺激而被广泛用于心理学和神经科学实验。主要目标是将ERP特征成分与受试者水平的协变量相关联。现有方法通常采用两步法，首先使用峰值检测方法识别ERP成分，然后将其与协变量关联。然而，这种方法可能由于初始步骤中的不准确估计而导致效率损失，尤其是在脑电图数据信噪比较低的情况下。为解决这一挑战，我们提出了一种半参数潜变量方差分析模型（SLAM），该模型统一了对ERP成分及其与协变量关联的推断。SLAM通过一种结构化的高斯过程先验对ERP波形进行建模，该先验在导数中编码ERP潜伏期，并使用潜变量方差分析将受试者水平的潜伏期与协变量相关联。这种统一的贝叶斯框架提供了群体水平和受试者水平的估计，通过跨受试者共享信息提高了推断效率。我们使用蒙特卡洛期望最大化算法自动化后验推断和超参数调优。通过模拟实验证明了SLAM相对于竞争方法的优势。我们的方法能够检验因素或协变量如何影响ERP成分的幅度和/或潜伏期，进而反映认知、心理或神经过程。我们通过一个语音识别ERP实验数据的应用实例加以说明，在该实验中评估了年龄对两个感兴趣成分的影响。我们的结果验证了科学发现：由于感知和大脑过程的延迟，老年人对外部刺激的反应时间更长。