Abstract
In the past three decades, the growth curve model (also known as latent curve model) has become a popular statistical methodology for the analysis of longitudinal or, more generally, repeated-measures data. Developed primarily within the latent variable modeling framework, the equivalent model emerged from other fields under the names of linear mixed-effects model, random-effects model, hierarchical linear model, and linear multilevel model. This methodology estimates the so-called growth parameters that describe individuals’ change trajectories across time and are related via linear combinations to the dependent variable. While satisfying in many research settings, oftentimes a linear relation between dependent variable and growth parameters cannot allow for meaningful interpretation of the growth parameters, parsimonious descriptions of the change phenomenon, good adjustment to the data across all values of the time predictor, and realistic extrapolations outside the empirical range of the time predictor. Consequently, nonlinear alternatives have been proposed, for which the growth parameters can be related to the dependent variable via any mathematical function (not just linear combinations). We discuss the theoretical foundations as well as practical implications of estimating nonlinear growth curve models. We also illustrate the methodology with an example from the psychological literature.
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Ghisletta, P., Cantoni, E., Jacot, N. (2015). Nonlinear Growth Curve Models. In: Stemmler, M., von Eye, A., Wiedermann, W. (eds) Dependent Data in Social Sciences Research. Springer Proceedings in Mathematics & Statistics, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-319-20585-4_2
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DOI: https://doi.org/10.1007/978-3-319-20585-4_2
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