Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being, spanning various metrics like physical activity (continuous), pain levels (truncated), mood states (ordinal), and life events (binary). These assessments, when categorized by time of day, become functional data of different types - continuous, truncated, ordinal, and binary. Inspired by this diversity, we introduce a unified approach called functional principal component analysis. It employs a semiparametric Gaussian copula model, assuming a generalized latent non-paranormal process as the underlying mechanism for these four types of functional data. We specify latent temporal dependence using a covariance estimated through Kendall's tau bridging method, incorporating smoothness during the bridging process. Simulation studies demonstrate the method's competitive performance under both dense and sparse sampling conditions. We then apply this approach to data from 497 participants in the National Institute of Mental Health Family Study of the Mood Disorder Spectrum to characterize within-day temporal patterns of mood differences among individuals with major mood disorder subtypes, including Major Depressive Disorder, Type 1, and Type 2 Bipolar Disorder.

翻译：移动健康研究常收集参与者行为和福祉的日内自我报告评估，涵盖体力活动（连续型）、疼痛程度（截断型）、情绪状态（有序型）及生活事件（二值型）等多类指标。这些按时段分类的评估数据构成了连续型、截断型、有序型和二值型等不同类别的函数型数据。受这种多样性启发，我们提出一种称为函数型主成分分析的统一方法。该方法采用半参数高斯连接函数模型，假设广义潜非平行过程作为这四类函数型数据的生成机制。通过基于肯德尔τ桥接方法估计的协方差矩阵来刻画潜变量的时域依赖结构，并在桥接过程中引入平滑约束。模拟研究表明，该算法在密集和稀疏采样条件下均表现优异。我们进一步将此方法应用于美国国家精神卫生研究院心境障碍谱系家族研究中497名参与者的数据，以刻画重度心境障碍亚型（包括重度抑郁症、I型及II型双相情感障碍）患者的日内情绪差异性时间模式。