Autoregressive Latent Trajectory (ALT) models: an assessment 25 years later

The Autoregressive Latent Trajectory (ALT) model was introduced at the 1999 Psychometric Society meeting (Bollen & Curran, 1999, 2004). Over the past 25 years, ALT models have become widely used for studying longitudinal dynamics, especially changes in multiple variables over time. Yet, their popularity has also generated confusion. Some published claims are contradictory, others are factually incorrect, and many emphasize the need for clearer explanations of the Classic and Latent-Variable ALT (LV-ALT) models. This paper explains the assumptions and structure of ALT models and clarifies how their parameters should be interpreted. It also supports both between- and within-component interpretations - contrary to assertions that such interpretations are impossible. We review prior literature on ALT properties and assess their accuracy. Further, we show the broad range of longitudinal models that are special cases of ALT models, enabling researchers to test and select the most suitable models for their data. An empirical example, previously used in multiple studies, illustrates these points. Overall, ALT and LV-ALT models provide a unifying framework for comparing many common longitudinal models. By clarifying their properties, correcting misconceptions, and demonstrating their applications, we aim to help researchers choose models that best reflect their theories and data.