Exploratory Latent Growth Models in the Structural Equation Modeling Framework

Abstract

Latent growth modeling is often conducted using a confirmatory approach whereby specific structures of individual change (e.g., linear, quadratic, exponential, etc.) are fit to the observed data, the best fitting model is chosen based on fit statistics and theoretical considerations, and parameters from this model are interpreted. This confirmatory approach is appropriate when a strong theory guides the model fitting process. However, this approach is often also used when there is not a strong theory to guide the model fitting process, which might lead researchers to misrepresent or miss key change characteristics present in their data. We discuss Tuckerized curves (Tucker, 1958, 1966) as an exploratory way of modeling change processes based on principal components analysis and propose an exploratory approach to latent growth modeling whereby minimal constraints are imposed on the structure of within-person change. These methods are applied to longitudinal data on cortisol response during a controlled experimental manipulation and height changes from early childhood through adulthood collected from 2 different studies. We highlight the additional insights gained, some of the benefits, limitations, and potential extensions of the exploratory growth curve approach and suggest there is much to be gained from using such models to generate new and potentially more precise theories about change and development.

Keywords:

• change
• cortisol
• development
• exploratory
• growth
• physical stature

Notes

¹We note that there are at least two alternative ways to specify these same exploratory growth models. One alternative specification involves fixing a factor loading at 1 for each factor and freeing its variance. This specification will have the same model fit as the specification described earlier because this is simply a respecification of identification constraints. And as in the previously described specification, growth factors are uncorrelated. A second alternative specification involves fixing R – 1 fixed factor loadings to 0 per growth factor and allowing the growth factors to correlate. Thus, a correlated solution is possible and, in many cases might be more reasonable. However, the trade-off comes in the form of additional fixed factor loadings—which might also constrain emergent interpretation of factor loading patterns. This specification leads to models that account for growth within specific phases of time, similar to spline or multiphase models, because each factor has a large number of 0 factor loadings. Although this is reasonable in some situations, specifying the model with uncorrelated factors allows for the estimation of more factor loadings and is closer to the Tuckerized curve approach.

²We thank Drs. Marilyn Albert and Teresa Seeman for making the data available to us.

*Indicates unique variance fixed at 0.000 in this model.