Advisor
Lalonde, Trent
Committee Member
Shafie, Khalil
Committee Member
Yu, Han
Department
Applied Statistics and Research Methods
Institution
University of Northern Colorado
Type of Resources
Text
Place of Publication
Greeley (Colo.)
Publisher
University of Northern Colorado
Date Created
12-2020
Extent
339 pages
Digital Origin
Born digital
Abstract
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.
Degree type
PhD
Degree Name
Doctoral
Language
English
Rights Statement
Copyright is held by the author.
