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Growth Curve Episode 5: Nonlinear Trajectories

The most basic form of growth model estimates a linear trajectory in which the model-implied change in the outcome is constant per unit-change in time. However, many constructs under study in the social and behavioral sciences follow nonlinear trajectories over time such that that the amount of change in the outcome depends on precisely when in time this change occurs... For example, there may be larger amounts of observed change between time 1 and 2, less change between time 5 and 6, and no change at all between time 9 and 10. Indeed, there may even be a point in time at which the direction of change reverses entirely. A common misunderstanding is that growth models can only incorporate functions that capture linear change over time, and this is actually not the case. In this episode of Office Hours Patrick explores three different approaches that allow for the estimation of nonlinear change within a growth model; all three methods are available in the structural equation approach to growth curve modeling, and two of three are available within the multilevel approach. Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling, 15, 513-533. Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling, 16, 676-701.