Multilevel Longitudinal Functional Principal Component Model.

Sensor devices, such as accelerometers, are widely used for measuring physical activity (PA). These devices provide outputs at fine granularity (e.g., 10-100 Hz or minute-level), which while providing rich data on activity patterns, also pose computational challenges with multilevel densely sampled data, resulting in PA records that are measured continuously across multiple days and visits. On the other hand, a scalar health outcome (e.g., BMI) is usually observed only at the individual or visit level. This leads to a discrepancy in numbers of nested levels between the predictors (PA) and outcomes, raising analytic challenges. To address this issue, we proposed a multilevel longitudinal functional principal component analysis (mLFPCA) model to directly model multilevel functional PA inputs in a longitudinal study, and then implemented a longitudinal functional principal component regression (FPCR) to explore the association between PA and obesity-related health outcomes. Additionally, we conducted a comprehensive simulation study to examine the impact of imbalanced multilevel data on both mLFPCA and FPCR performance and offer guidelines for selecting optimal methods.