Abstract
Structured latent curve models (SLCMs) for continuous repeated measures data have been the subject of considerable recent research activity. In this article, we develop a first-order SLCM for repeated measures count data where the underlying change process is theorized to develop in distinct phases. Parameters of the multiphase or piecewise growth model, including changepoints, are allowed to vary across individuals. Exposure is allowed to vary across both individuals and time. We demonstrate our modeling approach on empirical expressive language data (grammatical morpheme counts) drawn from multiple distinct corpora available in the Child Language Data Exchange System (CHILDES), where the acquisition of grammatical morphology is understood to occur in distinct phases in typically developing children. A multiphase SLCM is fit to summarize individuals' data as well as the average developmental pattern. Change in time-varying dispersion (unexplained variability in morpheme counts) over the course of early childhood is modeled concurrently to provide additional insights into acquisition. Unique characteristics of count data create modeling, identification, estimation, and diagnostic challenges that are exacerbated by incorporating growth models with nonlinear random effects. These are discussed at length. We provide annotated software code for each of models used in the empirical example.