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

Latent state-trait (LST) theory provides a psychometric framework that facilitates the measurement of long-term trait change and short-term state variability in longitudinal data. While LST theory has guided the development and extension of linear latent growth models within its theoretical framework, the integration of piecewise growth models (PGMs) into the LST theory framework remains uninvestigated. PGMs are well suited for modeling nonlinear developmental processes comprised of distinct stages, which frequently arise in psychological and educational research. Their ability to capture phase-specific changes makes them a useful tool for applied and methodological researchers. This paper introduces a novel measurement approach that integrates PGMs into the framework of LST theory by presenting single-indicator piecewise growth models (SI-PGMs) and multiple-indicator piecewise growth models (MI-PGMs). We detail the model specifications for both SI-PGMs and MI-PGMs. For SI-PGMs, we define the reliability coefficient; for MI-PGMs, we define the consistency coefficient, occasion specificity coefficient, and reliability coefficient. We then conduct simulations to evaluate the models' performance in accurately recovering growth parameters and capturing true reliability. The simulation results indicated that SI-PGMs and MI-PGMs successfully recovered growth parameters and performed comparably in the absence of situational influences. However, MI-PGMs outperformed SI-PGMs when situational influences were present. We conclude by outlining directions for future research and providing Mplus syntax to support the dissemination of the models.