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收集参与者每日多次自我报告的行为与健康评估数据。以一天内的时间为索引，这些评估可视为连续、截断、有序及二元类型的函数型观测。我们针对此类混合型函数型数据提出协方差估计与主成分分析方法。通过建立半参数高斯连接模型，该模型假设存在生成观测数据的广义潜在非正态过程，并以潜在协方差定义时间相关性。采用融合平滑步骤的Kendall Tau桥接方法构建潜在协方差的平滑估计，进而扩展该框架以处理稠密与稀疏两种采样设计，计算受试者特定观测数据潜在表征、潜在主成分及主成分得分。重要的是，该框架以统一方式处理全部四种混合数据类型。模拟研究表明，该方法在稠密与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庭研究的497名参与者数据，以刻画重型抑郁障碍、Ⅰ型及Ⅱ型双相障碍等主要情绪障碍亚型患者的日内情绪时间模式差异。