Specifying Piecewise Latent Trajectory Models for Longitudinal Data

Abstract Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when a simple model is needed to describe nonlinear change, or when the purpose of the analysis is to evaluate hypotheses about change occurring during a particular period of time within a model for a longer overall time frame, such as change that occurs following onset of a treatment or some other event. However, the specification of various forms of piecewise models has not been fully explicated for the structural equation modeling (SEM) framework. This article describes piecewise models as a straightforward extension of the basic SEM model for linear growth, which makes them relatively easy both to specify and to interpret. After presenting models for 2 linear slopes (or pieces) in detail, the article discusses extensions that include additional linear slopes (i.e., a 3-piece model) or a quadratic factor (i.e., a hybrid linear-quadratic model). ACKNOWLEDGMENTS I thank Laurie Chassin for sharing the alcohol use longitudinal data set, which was supported by Grant AA016213.