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.
Highlights
Longitudinal studies have been widely applied in many research areas to examine individual differences in growth over time
The study investigated the impacts of mis-specified turning point on growth trait estimation in conventional piecewise growth curve model (PGCM) that require turning points to be specified a priori
We examined the sensitivity of generally used model fit diagnostics [i.e., χ2 test statistic, root-mean-square error of approximation (RMSEA), Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), standardized root-meansquare residual (SRMR), modification index (MI), and SEPC] in detecting specification errors in conventional PGCMs due to turning points mislocation
Summary
Longitudinal studies have been widely applied in many research areas to examine individual differences in growth over time. The majority of applications of the latent growth models in longitudinal data analyses have been limited to the assumption that the change follows a simple linear trend. When longitudinal data are collected over an adequately long period of time, the features of individual change do not always follow a linear trend. A more flexible approach to model the nonlinear form of growth is the piecewise growth curve model (PGCM). This approach breaks up the curvilinear growth trend into separate linear segments or pieces of different slopes, which are tied together by turning points (or knots or change points). The approach is appealing when researchers are interested in comparing growth rates for two or more periods, such as the effect of schooling on children’s scholastic attainments before and after secondary school [7, 8]
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