A REGIME-SWITCHING (RS) FRAMEWORK FOR FORMULATING MULTI-PHASE LINEAR AND NONLINEAR GROWTH CURVE MODELS

In the past two decades, several approaches have been proposed for examining multi-phase longitudinal processes. These models include structural equation modeling variants of multiphase mixed effects models, in which specialized constraints are used to allow piecewise change functions to be represented as a single function in structural equation models (SEMs), with random effects appearing as latent variables. Another variant includes the sequential process growth mixture model, in which individuals are postulated to show piecewise change functions via transition through sequentially dependent latent classes. We discuss how these distinct but related frameworks may be conceived of as special cases of regime-switching SEMs, propose several new extensions within this modeling framework, and illustrate their respective strengths and limitations using a set of longitudinal reading and arithmetic performance data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998 (ECLS-K) study.