Abstract:
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This article addresses estimation in regression models for multilevel 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 linear mixed model representation. The process is empirically evaluated with several simulations and it is applied to analyze the physical activity data from the Active Schools Institute of the University of Northern Colorado.
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