First Advisor

Lalonde, Trent

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Date Created



In this study an intensive longitudinal functional model with multiple time-varying scales with scalar outcome, multiple functional predictors, one or more scalar covariates and subject-specific random intercepts through mixed model equivalence was proposed. 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 information 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. The simulation suggested that as the sample size and level of association were increased, mean square errors for functional coefficients were decreased. Furthermore, sample size had a larger impact for smaller level of association, and also level of association had a greater impact for smaller sample size. These results provided empirical evidence that the ILFMM estimates of functional coefficients were close to the true functional estimate (basically unchanged). Additionally, the results suggested that the AIC can be used to guide the choice of ridge weights. Also with sufficiently large ratios of ridge weights, there was minimal impact on the estimation performance. The proposed model with a single time scale was applied to analyze the physical activity data from the Active Schools Institute of the University of Northern Colorado to investigate what kind of time-structure patterns of activities could adequately describe the relationship between daily total magnitude and kids’ daily and weekly physical activities.


339 pages

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