Developing Dynamic Tools for Analyzing Intensive Longitudinal Data
Intensive longitudinal data have become increasingly prevalent in empirical studies. For instance, in the study of human emotions, researchers often adopt ecological momentary assessment (EMA) procedures to obtain responses reflecting individual’s ongoing emotional states “in the moment.” Common approaches for analyzing longitudinal data are not directly suited for handling the noisy, high-dimensional nature and diverse time scales of EMA affect data. The proposed project seeks to (1) develop and test frequentist and Bayesian estimation techniques for fitting discrete- and continuous-time dynamic models to intensive longitudinal data, (2) extend the models and estimation procedures to accommodate regime-switching processes, namely, processes that are characterized by phases with homogeneous dynamical structures, (3) conduct local influence analysis to assess the sensitivity of the proposed modeling procedures, and (4) find ways to improve the robustness of the estimation techniques in the presence of missing data. This project is supported by funding from the National Science Foundation.
Stochastic approximation expectation-maximization (SAEM) code for fitting linear/nonlinear ordinary differential equation models with random effects Download.
Code to implement Bayesian multi-resolution sampling algorithm for fitting nonlinear stochastic differential equation models. Download.
dynr (dynamic modeling in R). R package for fitting regime-switching linear and nonlinear dynamic models.
Chow, S. – M., Lu, Z., Sherwood, A., & Zhu, H.. (2016). Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm. Psychometrika, 81(1), 102 – 134. doi: 10.1007/s11336-014-9431-z
Chow, S. – M., Bendezú, J. J., Cole, P. M., & Ram, N.. (2016). A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects. Multivariate Behavioral Research, 51(2-3), 154 – 184. doi: 10.1080/00273171.2015.1123138
Lu, Z. – H., Chow, S. – M., Sherwood, A., & Zhu, H.. (2015). Bayesian analysis of ambulatory blood pressure dynamics with application to irregularly spaced sparse data. The Annals of Applied Statistics, 9(3), 1601 – 1620. doi: 10.1214/15-AOAS846 10.1214/15-AOAS846SUPP