A multilevel Ornstein-Uhlenbeck process with individual- and variable-specific estimates as random effects.

Area of Science:

• Statistics
• Time Series Analysis
• Bayesian Inference

Background:

• The Ornstein-Uhlenbeck (OU) process is a stationary Gauss-Markov model for time series.
• Analyzing multiple variables simultaneously presents analytical challenges.

Purpose of the Study:

• To extend the OU process for simultaneous analysis of multiple time series.
• To incorporate random effects for individuals and variables within a Bayesian framework.
• To estimate parameter variability across individuals and variables.

Main Methods:

• Developed a multilevel OU process using a Bayesian framework.
• Utilized marginalized posterior distributions to estimate parameter variability.
• Applied the model to affect dynamics data and conducted simulation studies.

Main Results:

• The multilevel OU process successfully estimates general and variable-specific parameters.
• Simulation studies confirmed the model's ability to recover population parameters.
• Demonstrated the interpretability of parameters in affect dynamics.

Conclusions:

• The proposed multilevel OU process is effective for simultaneous multi-variable time series analysis.
• It provides valuable insights into individual and variable-specific dynamics.
• This approach offers a robust tool for complex time series data.