On the Correspondence between the Latent Growth Curve and Latent Change Score Models

There has been a great deal of work in the literature on the equivalence between the mixed-effects modeling and structural equation modeling (SEM) frameworks in specifying growth models (Willett & Sayer, 1994). However, there has been little work on the correspondence between the latent growth curve model (LGM) and the latent change score model (see Grimm, Zhang, Hamagami, & Mazzocco, 2013). We demonstrate that four popular variants of the latent change score model - the no change, constant change, proportional change, and dual change models - have LGM equivalents. We provide equations that allow the translation of parameters from one approach to the other and vice versa. We then illustrate this equivalence using mathematics achievement data from the National Longitudinal Survey of Youth.