Application of growth model applying GAMM and PGM

Exploring a growth model in a longitudinal study is as important as verifying the effectiveness of variables related to growth. In this study, in identifying the growth model, the analysis was conducted using the generalized additive mixed model (GAMM) and the piecewise growth model (PGM) in longitudinal study. For empirical data, GAMM and PGM were used for identifying changes in students' academic achievement in mathematics through the Korean Education Longitudinal Study (KELS-2013) data. As a result, the exponent of the growth model function optimized in GAMM was calculated as 2.98, confirming that the growth model was most suitable for a cubic function. In addition, as a result of verifying the random effect by applying GAMM, a growth of 198.73 points was confirmed in the first year, the starting point of the survey, and it was confirmed that female students showed 2.97 points higher growth than male students in terms of growth in students' math achievement. On the other hand, as a result of applying PGM, the turning point appeared at 2.54, and it was confirmed that the greatest change was shown at the time of school grade change from elementary school to middle school. Such results as in this study show different approaches through GAMM and PGM to explore data-based growth models, and these results can be greatly expanded to analyze growth models such as data-based machine learning methods.