Chapter 7: Finite Mixtures Of Nonlinear Mixed-Effects Models

Nonlinear patterns of change arise frequently in the analysis of repeated measures from longitudinal studies in the behavioral and social sciences and, as a consequence, practitioners have begun turning with more frequency to methods that can incorporate intrinsically nonlinear functions into an analysis. In contrast to linear processes, which assume steady incremental change across time or other condition, the cornerstone of nonlinear development is that change occurs more quickly in some periods than in others. Furthermore, there is often an implicit understanding that a nonlinear function can be identified—either grounded in theory, derived empirically from an initial exploration of the data, or both—that effectively summarizes the repeated measures and whose parameters capture important facets of the underlying process. The nonlinear mixed-effects (NLME) model (Davidian & Giltinan, 1995; Pinheiro & Bates, 2000) has become a popular platform for the analysis of continuous repeated-measures data with these notable characteristics where primary interest focuses on individual-level change.