International Society for Data Science and Analytics, Data Science and Psychology - 2024 Meeting of ISDSA

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Piecewise Strategies for Fitting Differential Equation Models to Time Series Data
Yueqin Hu

Date: 2024-07-23 10:30 AM – 11:00 AM
Last modified: 2024-07-05

Abstract


Differential equation models are continuous-time dynamic models suitable for analyzing intensive longitudinal data. Numerical optimization methods can be used to estimate parameters in differential equation models. However, as behavioral data often exhibit phase jumps, and longer time series are more prone to phase jumps, this method can lead to inaccurate estimation when applied to behavioral data, especially long sequences. Therefore, this study proposes segmenting the time series data to accurately estimate long sequences with phase problems. The method we propose allows each short segment of the long sequence to use different initial values, thus enabling more accurate capture of local dynamics, and then estimating overall fixed effects and local random effects accordingly using the multilevel version of the numerical optimization method. Data simulation conditions include time series length, signal-to-noise ratio, and phase jump conditions, and the segmentation algorithm considers smoothing methods, sliding window width, and step size. We will present the performance of different segmentation methods compared to the non-segmentation algorithms under various data conditions, and provide empirical demonstrations using intensive longitudinal data on mindfulness and psychological distress from two hundred and seventy university students at thirty-five consecutive time points.

Keywords


Longitudinal Data

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