Switching principal component analysis for modeling means and covariance changes over time.

Area of Science:

• Psychology
• Statistics
• Physiology

Background:

• Psychological theories posit that cognitions, affect, and action tendencies change over time.
• These changes can be abrupt, driven by specific events, and manifest in both mean levels and covariance structures of variables.
• Analyzing these dynamic changes in multivariate time series data presents challenges, including unknown phase numbers and start times, and complex covariance patterns.

Purpose of the Study:

• To introduce switching principal component analysis (PCA) as a method to detect phases with similar means and/or covariation structures in single-subject multivariate time series.
• To provide an algorithm for fitting switching PCA solutions and a model selection procedure.
• To evaluate the performance of switching PCA through a simulation study and analyze empirical cardiorespiratory data.

Main Methods:

• Switching principal component analysis (PCA) is proposed to identify distinct phases within multivariate time series data.
• The method performs PCA within each detected phase to understand its specific covariance structure.
• An accompanying algorithm for fitting solutions and a model selection procedure are developed and tested.

Main Results:

• Switching PCA successfully detects phases characterized by similar means and/or covariation structures.
• The method facilitates the interpretation of covariance patterns within identified phases.
• The simulation study and empirical data analysis demonstrate the utility of switching PCA.

Conclusions:

• Switching PCA offers a robust approach for analyzing dynamic changes in multivariate time series data.
• The method aids in understanding abrupt shifts in psychological and physiological variables.
• This technique enhances the interpretability of complex, time-varying data structures.