Generalized Multilevel Functional Principal Component Analysis with Application to NHANES Active Inactive Patterns

Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. In this study, we analyze minute-level indicators of being active, which can be viewed as binary (since each minute is either active or inactive), multilevel (because there are multiple days of data for each participant), and functional data (because the within-day measurements can be viewed as a function of time). To identify both within- and between-participant directions of variation in these data, we introduce Generalized Multilevel Functional Principal Component Analysis (GM-FPCA), an approach based on the dimension reduction of the linear predictor. Our results indicate that specific activity patterns captured by GM-FPCA are strongly associated with mortality risk. Extensive simulation studies demonstrate that GM-FPCA accurately estimates model parameters, is computationally stable, and scales up with the number of study participants, visits, and observations per visit. R code for implementing the method is provided.