Linear-linear piecewise growth mixture models with unknown random knots: A primer for school psychology

Studying change over time requires rigorous and sometimes novel statistical methods that can support increasingly complex applied research questions. In this article, we provide an overview of the potential of piecewise growth mixture models. This type of longitudinal model can be used to advance our understanding of group and individual growth that may follow a segmented, or disjointed, pattern of change, and where the data come from a mixture of two or more latent classes. We then demonstrate the practical utility of piecewise growth mixture models by applying it to a subsample of students from the Early Childhood Longitudinal Study - Kindergarten Cohort of 1998 (ECLS-K) to ascertain whether mathematics achievement is characterized by one or two latent classes akin to students with and without mathematics difficulties. We discuss the applicability for school psychological research and provide supplementary online files that include an instructional sample dataset and corresponding R routine with explanatory annotations to assist in understanding the R routine before applying this approach in novel applications (https://doi.org/10.1016/j.jsp.2019.03.004).