A Study of Latent State-Trait Theory Framework in Piecewise Growth Models

Area of Science:

• Psychometrics
• Longitudinal Data Analysis
• Developmental Psychology

Background:

• Latent State-Trait (LST) theory offers a framework for analyzing long-term trait change and short-term state variability in longitudinal data.
• Existing LST applications primarily focus on linear latent growth models, leaving the integration of nonlinear models unexplored.
• Piecewise growth models (PGMs) are suitable for capturing distinct stages in nonlinear developmental processes common in psychological and educational research.

Purpose of the Study:

• To introduce a novel measurement approach integrating PGMs into the LST theory framework.
• To present and detail the specifications for single-indicator PGMs (SI-PGMs) and multiple-indicator PGMs (MI-PGMs) within LST theory.
• To evaluate the performance of SI-PGMs and MI-PGMs in recovering growth parameters and reliability through simulations.

Main Methods:

• Development of single-indicator piecewise growth models (SI-PGMs) and multiple-indicator piecewise growth models (MI-PGMs) within the LST framework.
• Definition of key coefficients: reliability for SI-PGMs; and consistency, occasion specificity, and reliability for MI-PGMs.
• Conducting simulation studies to assess parameter recovery and reliability estimation accuracy under varying conditions.

Main Results:

• Both SI-PGMs and MI-PGMs demonstrated success in recovering growth parameters and reliability when no situational influences were present.
• MI-PGMs exhibited superior performance compared to SI-PGMs in accurately capturing growth parameters and reliability when situational influences were introduced.
• Simulation results confirmed the viability of integrating PGMs into the LST framework for longitudinal data analysis.

Conclusions:

• The integration of PGMs into LST theory provides a valuable tool for analyzing nonlinear developmental trajectories.
• MI-PGMs offer enhanced accuracy and robustness, particularly in the presence of situational influences, compared to SI-PGMs.
• The proposed models and accompanying Mplus syntax facilitate broader application in psychological and educational research for nuanced longitudinal analysis.