Chapter 2: On Interpretable Reparameterizations of Linear and Nonlinear Latent Growth Curve Models

One of the primary goals of longitudinal modeling is to estimate and interpret free model parameters that reflect meaningful aspects of change over time in a parsimonious manner. Perhaps the simplest example is to estimate a linear slope in regression analysis when the predictor is time (t) and the criterion (y) is measured repeatedly at several occasions; this slope may be interpreted straightforwardly as the expected change in y given a unit change in t in the population, holding constant all other predictors. Of course, the nature of longitudinal change may be far from this simplest scenario, and as such researchers are increasingly seeking theoretically appropriate ways to model more complex nonlinear systems as well (see, e.g., Grimm & Ram, 2009; Ram & Grimm, 2007).