Specifying Turning Point in Piecewise Growth Curve Models: Challenges and Solutions - Ning, Ling; Luo, Wen (Frontiers in Applied Mathematics and Statistics, 2017)
Piecewise growth curve model (PGCM) is often used when the underlying growth process is not linear and is hypothesized to consist of phasic developments connected by turning points (or knots or change points). When fitting a PGCM, the conventional practice is to specify turning points a priori. However, the true turning points are often unknown and misspecifications of turning points may occur. The study examined the consequences of turning point misspecifications on growth parameter estimates and evaluated the performance of commonly used fit indices in detecting model misspecification due to mis-specified locations of turning points. In addition, this study introduced and evaluated a newly developed PGCM which allows unknown turning points to be freely estimated. The study found that there are severe consequences of turning point misspecification. Commonly used model fit indices have low power in detecting turning point misspecification. On the other hand, the newly developed PGCM with freely estimated unknown turning point performs well in general.