We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by estimating the principal components of the covariance matrix on the linear predictor scale conditional on the fixed effects. This is achieved by combining three modeling innovations: (1) fit local generalized linear mixed models (GLMMs) conditional on covariates in windows along the functional domain; (2) conduct a functional principal component analysis (FPCA) on the person-specific functional effects obtained by assembling the estimated random effects from the local GLMMs; and (3) fit a joint functional mixed effects model conditional on covariates and the estimated principal components from the previous step. GC-FPCA was motivated by modeling the minute-level active/inactive profiles over the day ($1{,}440$ 0/1 measurements per person) for $8{,}700$ study participants in the National Health and Nutrition Examination Survey (NHANES) 2011-2014. We show that state-of-the-art approaches cannot handle data of this size and complexity, while GC-FPCA can.

翻译：本文提出广义条件函数主成分分析（GC-FPCA），用于非高斯函数型结果的固定效应与随机效应的联合建模。该方法通过在线性预测尺度上估计协方差矩阵的主成分（以固定效应为条件），可扩展至超大规模函数型数据集。这一目标通过结合三项建模创新实现：（1）在函数域上的滑动窗口内，以协变量为条件拟合局部广义线性混合模型（GLMM）；（2）对通过整合局部GLMM估计的随机效应所获得的个体特异性函数效应进行函数主成分分析（FPCA）；（3）以协变量及前一步估计的主成分为条件，拟合联合函数混合效应模型。GC-FPCA的提出源于对美国国家健康与营养调查（NHANES）2011-2014年度8,700名研究参与者日内分钟级活动/非活动剖面（每人1,440个0/1测量值）的建模需求。我们证明现有前沿方法无法处理此类规模与复杂度的数据，而GC-FPCA可以胜任。