Piecewise Linear–Linear Latent Growth Mixture Models With Unknown Knots

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear–linear latent growth mixture model (LGMM) for describing segmented change of individual behavior over time where the data come from a mixture of two or more unobserved subpopulations (i.e., latent classes). Thus, the focus of this article is to illustrate the practical utility of piecewise linear–linear LGMM and then to demonstrate how this model could be fit as one of many alternatives—including the more conventional LGMMs with functions such as linear and quadratic. To carry out this study, data (N = 214) obtained from a procedural learning task research were used to fit the three alternative LGMMs: (a) a two-class LGMM using a linear function, (b) a two-class LGMM using a quadratic function, and (c) a two-class LGMM using a piecewise linear–linear function, where the time of transition from one phase to another (i.e., knot) is not known a priori, and thus is a parameter to be estimated.