comparison of three growth modeling techniques in the multilevel analysis of longitudinal academic achievement scores: Latent growth modeling, hierarchical linear modeling, and longitudinal profile analysis via multidimensional scaling

Growth trajectories of mathematics achievement: Longitudinal tracking of student academic progress

“…Whereas previous studies tended to investigate growth in terms of average change across time for groups or cohorts, sustained intra‐individual growth deserves special attention from an educational perspective (Anderman et al ., ; Martin, , ; Martin & Liem, ; Murayama et al ., ). Recent developments in statistical methods, including hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS), facilitated studies of intra‐individual, as well as interindividual, growth (Anderman et al ., ; Grimm & Ram, ; Muthén & Khoo, ; Shin, , ; Shin et al ., ). In a 4‐year longitudinal study involving 1,244 students, Shin () employed HLM, LGM, and LPAMS models to describe the growth trajectories of students from Grade 2 to Grade 5.…”

“…Recent developments in statistical methods, including hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS), facilitated studies of intra‐individual, as well as interindividual, growth (Anderman et al ., ; Grimm & Ram, ; Muthén & Khoo, ; Shin, , ; Shin et al ., ). In a 4‐year longitudinal study involving 1,244 students, Shin () employed HLM, LGM, and LPAMS models to describe the growth trajectories of students from Grade 2 to Grade 5. Each of these methods was found to have application potential for different research designs and data structures, but LGM was recommended for longitudinal studies with a large sample size and nested data structure due to its flexibility (Shin, ).…”

Multilevel analysis of the effects of student and course characteristics on satisfaction in undergraduate liberal arts courses

“…On the other hand, if the mean score of each class were used, an aggregation bias appears. In order to solve these problems, a hierarchical linear model (HLM), which analyzes not only student-level data but also course-level data, might be more appropriate (Chin, 2007;Civian & Brennan, 1996;Nasser & Hagtvet, 2006;Raudenbush & Bryk, 2002;Tabachnick & Fidell, 2007;Ting, 2000;Umbach & Porter, 2002). The HLM is a data analysis technique for research designs where the data for participants is organized at more than one level.…”

Longitudinal tracking of academic progress during teacher preparation

“…Nonetheless, the between‐semester variation was smaller than the variations within‐semester. Further, there were indications of heterogeneous error variance of measurement over time, providing added justification for selection of LGM over other methods (Shin, ).…”

“…Shin () conducted a 4‐year longitudinal study that comprised 1,244 students that utilized hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS) in order to detail the growth in student achievement trajectories from Grade 2 to Grade 5. Shin's results supported the use of LGM for longitudinal research with nested data and large sample sizes.…”