Growth modeling within a structural equation modeling framework

In a prior episode of Office Hours, Patrick explored “Growth modeling in a multilevel modeling framework.” In the current episode he discusses how growth models can also be estimated within the structural equation modeling (SEM) framework. He begins with a brief review of the confirmatory factor analysis model and describes this as the foundation of the latent curve model (LCM) estimated within the SEM. He explains the motivation for using the observed repeated measures as multiple indicators defining one or more underlying latent growth factors. He then describes using this formulation to estimate an LCM that he then extends to include time-invariant and time-varying covariates. He concludes with a brief description of multivariate LCMs that allow for the simultaneous estimation of growth processes in two or more constructs at once.

To see all episodes in this series, see our Growth Modeling playlist.

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A reviewer recently asked me to comment on the issue of equivalent models in my structural equation model. What is the difference between alternative models and equivalent models within an SEM?

An equivalent model can be thought of as a re-parameterization of the original model. In other words, it is just a different way of “packaging” the same information in the data and no equivalent model can be distinguished from another based on fit alone. If you were to fit a series of equivalent models to the same sample data you obtain exactly the same chi-square test statistic, RMSEA, CFI, TLI, and any other omnibus measure of fit. It is often best to treat this as a limitation of any given study and to potentially present one or a small number of equivalent model options to the reader so that these too might be considered as plausible representations of the data.

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