Specifying Turning Point in Piecewise Growth Curve Models: Challenges and Solutions

Abstract

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.

The Development of Motivation and Amotivation to Study and Work across Age-Graded Transitions in Adolescence and Young Adulthood

“…To answer the research questions, piecewise growth curve models (PGCM) were computed in Mplus version 8.0. In piecewise growth curve models, researchers identify a turning point or knot in a curvilinear growth trend and use this to separate the trend into separate slopes, to compare them (Ning & Luo, 2017). This presents an ideal model to test growth across the mid-schooling transition (W1 -W3) versus across the school-to-work transition (W3 -W5).…”

Reconciling Theory and Context in Comparative Nonprofit Research

“…In some cases, analysts might not know the turning points and need to discover them inductively. A recent paper by Ning and Luo (2017) gives some directions on how this might be done. 9 A second issue is that national-level contextual effects are often endogenous, and simultaneity is often the cause.…”

Longitudinal measurement invariance and stability of individual interest across a 16‐week introductory animal sciences course

“…Although the sample size of the Spring 2019 cohort was roughly half that of the Fall 2018 cohort, the large fraction of residual variance indicated that misfit derived from misspecification—the linear and quadratic shape parameters did not describe the data well. Although it is possible to specify more complex shape parameters in LGCM, this approach extended beyond our objectives and was not suggested by our data (Ning & Luo, 2017). As a result, we concluded that Spring 2019 individual interest showed no consistent shape patterns, and its trajectory was obscured substantially by both within‐ and between‐individual variation.…”