Comparison of Latent Growth Curves: A Parameter Constancy Test
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Authors
Rosel, Jesús
Puchol, Sara
Elipe, Marcel
Flor, Patricia
Machancoses, Francisco
Canales, Juan
Supervisor
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Journal Article
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Publisher
American Psychological Association
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).Description
Keywords
5201 Applied and Developmental Psychology, 5205 Social and Personality Psychology, 49 Mathematical Sciences, 4905 Statistics, 52 Psychology, 1701 Psychology, 1702 Cognitive Sciences, Social Sciences Methods, 5201 Applied and developmental psychology, latent growth curves, parameter constancy test, structural stability, model comparison, structural equation modeling
Source
Psychological methods, ISSN: 1082-989X (Print); 1939-1463 (Online), American Psychological Association. doi: 10.1037/met0000788
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© 2025 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0; https://creativecommons.org/licenses/by/4.0). This license permits copying and redistributing the work in any medium or format, as well as adapting the material for any purpose, even commercially.