Longitudinal functional models with structured penalties

This article addresses estimation in regression models for longitudinally collected functional covariates (time-varying predictor curves) with a longitudinal scalar outcome. The framework consists of estimating a time-varying coefficient function that is modelled 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 human immunodeficiency virus (HIV) patients and its association with longitudinally-collected magnetic resonance spectroscopy (MRS) curves.