Statistical Modelling 16 (2) (2016), 114–139

Longitudinal functional models with structured penalties

Madan G. Kundu
Novartis Pharmaceuticals Corporation (Oncology),
East Hanover, NJ,

Jaroslaw Harezlak
Department of Biostatistics,
Indiana University RM Fairbanks School of Public Health, IN,

Timothy W. Randolph
Biostatistics and Biomathematics Program,
Fred Hutchinson Cancer Research Center, WA,


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.


functional data analysis; Longitudinal data; LongPEER estimate; structured penalty; generalized singular value decomposition.


Code in zipped archive. The data are available on request from the authors.