On the Trajectories of the Predetermined ALT Model: What Are We Really Modeling?

Abstract

This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a linear trajectory might be present among the model predicted scores even though no latent change parameter was included in the model. In addition, 2 examples are given that show that the predetermined ALT model can fit to data generated by models with model structures that are rather different from that of the ALT model itself. The practical relevance of these findings is demonstrated using an empirical example. We end by providing recommendations for researchers considering the use of the predetermined ALT model.