Longitudinal Functional Models with Structured Penalties

This paper addresses estimation in a longitudinal regression model for association between a scalar outcome and a set of longitudinally-collected functional covariates or predictor curves. The framework consists of estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions but having time-varying coefficients. 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 curves.