Reconsidering the Use of Autoregressive Latent Trajectory (ALT) Models

The simultaneous estimation of autoregressive (simplex) structures and latent trajectories, so called ALT (autoregressive latent trajectory) models, is becoming an increasingly popular approach to the analysis of change. Although historically autoregressive (AR) and latent growth curve (LGC) models have been developed quite independently from each other, the underlying pattern of change is often highly similar. In this article it is shown that their integration rests on the strong assumption that neither the AR part nor the LGC part contains any misspecification. In practice, however, this assumption is often violated due to nonlinearity in the LGC part. As a consequence, the autoregressive (simplex) process incorrectly accounts for part of this nonlinearity, thus rendering any substantive interpretation of parameter estimates virtually impossible. Accordingly, researchers are advised to exercise extreme caution when using ALT models in practice. All arguments are illustrated by empirical data on skill acquisition, and a simulation study is provided to investigate the conditions and consequences of mistaking nonlinear growth curve patterns as autoregressive processes.