This article addresses estimation in regression models for longitudinally-collected functional covariates (time-varying predictor curves) with a longitudinal scaler outcome. The framework consists of estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions with time-varying coefficients. The model uses extrinsic information to inform the structure of the penalty, while the estimation procedure exploits the equivalence between penalized least squares estimation and a linear mixed model representation. The process is empirically evaluated with several simulations and it is applied to analyze the neurocognitive impairment of HIV patients and its association with longitudinally-collected magnetic resonance spectroscopy (MRS) curves.
Keywords: Functional data analysis; LongPEER estimate; generalized singular value decomposition; longitudinal data; structured penalty.