Comparison of Latent Growth Curves: A Parameter Constancy Test

Abstract

Latent growth curve (LGC) models, implemented through structural equation modeling, are widely used to analyze developmental and learning trajectories. Model selection in LGC often relies on goodness-of-fit indices (e.g., χ², Akaike information criterion, and root-mean-square error of approximation), but these metrics fail to assess the temporal constancy, or stability of parameters, an important aspect when forecasting longitudinal data. Addressing this gap, we propose a novel parameter constancy test (PCT) tailored for LGC models. This test evaluates internal constancy, identifies potential breakpoints, helps determine the minimal number of measurement waves needed for reliable modeling, and is also useful for comparing different explanatory models of the analyzed data. To validate this approach, we applied PCT to real-world data, comparing the widely used quadratic function model with the negative exponential model and other nonlinear functions. The results reveal that the negative exponential model, unlike the quadratic function, consistently exhibits parameter constancy even with fewer sampling waves, making it particularly suitable for longitudinal analysis. Additionally, PCT highlights how inappropriate model selection or instability may lead to misinterpretations, particularly in evaluating interventions or extrapolating beyond observed time frames. Our findings emphasize the dual importance of statistical fit and parameter constancy in selecting LGC models. By integrating PCT into standard practice, researchers can better ensure model consistency, optimize resource allocation, and avoid erroneous conclusions in developmental and learning studies. (PsycInfo Database Record (c) 2025 APA, all rights reserved).