Dynamic Models for Intensive Longitudinal Data: New Models, Statistical Procedures, and Applications

Open Access
Author:
Trail, Jessica Brooke
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 15, 2014
Committee Members:
  • Linda Marie Collins, Dissertation Advisor
  • Runze Li, Dissertation Advisor
  • John Fricks, Committee Member
  • Donna Coffman, Committee Member
Keywords:
  • intensive longitudinal data
  • dynamic systems
  • time-varying effects
Abstract:
Functional data analysis (FDA) of intensive longitudinal data is becoming increasingly popular in the behavioral sciences to study time-varying processes. This dissertation focuses on integrating two methods which are useful in FDA: dynamical systems models and time-varying coefficient models. Dynamic models provide a more detailed description of a time-varying process than some traditional longitudinal data methods, including effects that characterize the shape, magnitude, and speed of the outcome’s response to a change in inputs, or predictors. Allowing these effects to vary as functions of time uses the intensive nature of the data to describe even more complex change. In the behavioral sciences, a better understanding of the dynamics of a process could be used to inform the design of behavioral interventions. For example, this dissertation was motivated by a study designed to examine the trajectories of change in students’ smoking behavior during the freshman year of college. A better understanding of the trajectory of smoking onset will help inform the development of behavioral interventions to alter this trajectory and prevention smoking. This is important because smoking is the leading preventable cause of death in the US. The repeated measurements used to describe a dynamical system frequently contain measurement error, and so statistical methods are needed to estimate the parameters of the differential equation model. In this dissertation, we propose a two-step estimation method. The first step uses spline smoothers to smooth the noisy observed data and estimate the derivatives. The second step uses penalized splines to estimate the time-varying effects in the differential equation. We use simulated data to describe the performance of the proposed estimation method. To test hypotheses about the time-varying effects, for example, whether or not an effect is significantly time-varying or determining if a covariate is significant in the model, we propose a generalized likelihood ratio test statistic. We use bootstrap methods and a Monte Carlo simulation study to assess the finite sample properties of the proposed test statistic. The proposed methodology is applied to data from the UpTERN study (Tiffany, et al., 2004). In this empirical example, we examine and test hypotheses about the relations between covariates such as alcohol use and gender and the dynamics of cigarette smoking.