A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional...

Area of Science:

• Psychology
• Quantitative Psychology
• Behavioral Science

Background:

• Traditional psychological research often focuses on the mean structure of temporal development.
• Within-person variability research has historically lacked sophisticated modeling approaches.
• Multivariate GARCH models, common in finance, offer a novel framework for psychological data.

Purpose of the Study:

• To adapt and evaluate multivariate GARCH (MGARCH) models for analyzing within-person variability in psychological research.
• To introduce new parameterizations for MGARCH models, specifically pdBEKK and DCC, to incorporate time-varying predictors.
• To assess the utility of these models for understanding individual differences in psychological constructs.

Main Methods:

• Proposed novel pdBEKK and modified DCC models derived from financial MGARCH.
• Incorporated external time-varying predictors for within-person variance.
• Applied models to daily positive and negative affect data from two individuals over 100 days.
• Included a multivariate ARMA(1,1) for means and physical activity as a moderator.

Main Results:

• MGARCH models partition within-person variance into baseline, innovation-conditional, and carry-over components.
• Both pdBEKK and DCC models demonstrated potential for analyzing within-person variability.
• pdBEKK offered more intuitive psychological interpretation, while DCC was easier to estimate and handled more series.
• Sufficient data points are crucial for detecting significant parameters in both models.

Conclusions:

• MGARCH models provide a valuable framework for advancing the study of within-person variability in psychology.
• The developed pdBEKK and DCC models offer flexible approaches to modeling psychological time-series data.
• An R-package 'bmgarch' is provided to facilitate the application of these advanced statistical techniques.