• An Iterative Procedure to Select and Estimate Wavelet-Based Functional Linear Mixed-Effects Regression Models

      Lundeen, Jordan Sarah; Biostatistics (Augusta University, 2019-12)
      Actigraphy is the continuous long-term measurement of activity-induced acceleration by means of a portable device that often resembles a watch and is typically worn on the wrist. Actigraphy is increasingly being used in clinical research to measure sleep and activity rhythms that might not otherwise be available using traditional techniques such as polysomnography. Actigraphy has been shown to be of value when assessing circadian rhythm disorders and sleep disorders and when evaluating treatment outcomes. It can provide more objective information on sleep habits in the patient's natural sleep environment than using the patient's recollection of their activity or a written sleep diary. We propose a wavelet-based functional linear mixed model to investigate the impact of functional predictors on a scalar response when repeated measurements are available on multiple subjects. The advantage of the proposed model is that each subject has both individual scalar covariate effects and individual functional effects over time, while also sharing common population scalar covariate effects and common population slope functions. An iterative procedure is used to estimate and select the fixed and random effects by utilizing the partial consistency property of the random effect coefficients and selecting groups of random effects simultaneously via the smoothly clipped absolute deviation (SCAD) penalty function. In the first study of its kind, we compare multiple functional regression methods through a large number of simulation parameter combinations. The proposed model is applied to actigraphy data to investigate the effect of daily activity on Hamilton Rating of Depression Scale (HRSD), Insomnia Severity Index (ISI) and Reduced Morningness- Eveningness Questionnare (RMEQ) scores.