Mobile digital health (mHealth) studies often collect multiple within-day self-reported assessments of participants' behaviour and health. Indexed by time of day, these assessments can be treated as functional observations of continuous, truncated, ordinal, and binary type. We develop covariance estimation and principal component analysis for mixed-type functional data like that. We propose a semiparametric Gaussian copula model that assumes a generalized latent non-paranormal process generating observed mixed-type functional data and defining temporal dependence via a latent covariance. The smooth estimate of latent covariance is constructed via Kendall's Tau bridging method that incorporates smoothness within the bridging step. The approach is then extended with methods for handling both dense and sparse sampling designs, calculating subject-specific latent representations of observed data, latent principal components and principal component scores. Importantly, the proposed framework handles all four mixed types in a unified way. Simulation studies show a competitive performance of the proposed method under both dense and sparse sampling designs. The method is applied to data from 497 participants of National Institute of Mental Health Family Study of the Mood Disorder Spectrum to characterize the differences in within-day temporal patterns of mood in individuals with the major mood disorder subtypes including Major Depressive Disorder, and Type 1 and 2 Bipolar Disorder.

翻译：移动数字健康研究常采集参与者行为和健康的多项日内自我报告评估数据。这些以每日时刻为索引的评估数据可视为连续型、截断型、有序型和二元型的函数型观测。针对此类混合型函数型数据，我们发展了协方差估计与主成分分析方法。提出半参数高斯连接函数模型，该模型假设存在一个广义潜在非正态高阶过程生成观测混合型函数型数据，并通过潜在协方差定义时间依赖性。采用融合平滑步骤的肯德尔τ桥接方法构建潜在协方差的平滑估计。该方法进一步扩展至处理密集与稀疏采样设计，可计算观测数据的受试者特异性潜在表征、潜在主成分及主成分得分。值得注意的是，该框架以统一方式处理所有四种混合类型。仿真研究表明，该方法在密集和稀疏采样设计下均具有竞争力。我们将该方法应用于美国国家精神卫生研究所情绪障碍谱系家族研究中497名参与者的数据，以刻画包括重性抑郁障碍、Ⅰ型与Ⅱ型双相障碍在内的主要情绪障碍亚型患者日内情绪时间模式的差异特征。