Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories

We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of rates of change and acceleration in latent growth curvesinformation available indirectly through traditional growth curve models when change patterns are nonlinear with respect to time. To illustrate this approach, exponential growth models in the three frameworks are fit to longitudinal response time data from the Math Skills Development Project (Mazzocco & Meyers, 2002, 2003). We highlight the additional information gained from fitting growth curves in these frameworks as well as limitations and extensions of these approaches.