Specifying piecewise latent trajectory models for longitudinal data

Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when U Simple model is needed to describe nonlinear change, or when the purpose of (lie 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 it treatment 01, 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).