A Square-Root Second-Order Extended Kalman Filtering Approach for Estimating Smoothly Time-Varying Parameters
Zachary F Fisher1, Sy-Miin Chow2, Peter C M Molenaar2
1Department of Psychology and Neuroscience, University of North Carolina at Chapel Hill.
Multivariate Behavioral Research
|October 7, 2020
Summary
This study introduces a novel Kalman filtering method to model complex, time-varying psychological dynamics in intensive longitudinal data (ILD). The approach accurately captures emotional changes and intervention effects over time.
Area of Science:
- Psychological science
- Statistics
- Time series analysis
Background:
- Intensive longitudinal data (ILD) is crucial for understanding dynamic psychological processes.
- Existing models often fail to capture the complex, time-varying nature of these processes.
- Characterizing intervention effects on individual behavior requires models that account for temporal dynamics.
Purpose of the Study:
- To introduce a Square-Root Second-Order Extended Kalman Filtering approach for estimating smoothly time-varying parameters.
- To address limitations in modeling complex, time-dependent psychological phenomena.
- To provide a method capable of handling dynamic factor models with evolving relationships.
Main Methods:
- Developed a Square-Root Second-Order Extended Kalman Filtering algorithm.
- Applied the algorithm to dynamic factor models with time-varying parameters.
- Utilized Monte Carlo simulations to evaluate algorithm performance.
Main Results:
- The proposed Kalman filtering approach accurately recovers unobserved states in bivariate dynamic factor models.
- Demonstrated effectiveness in scenarios with time-varying dynamics and treatment effects.
- Successfully characterized the time-varying impact of a meditation intervention on emotional experiences.
Conclusions:
- The Square-Root Second-Order Extended Kalman Filtering approach offers a robust method for analyzing time-varying parameters in ILD.
- This method enhances the ability to model complex psychological dynamics and intervention effects.
- Provides a valuable tool for researchers studying dynamic systems and behavioral changes over time.
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