방법 비교

	Educational Growth Curve Modeling	Educational Hierarchical Linear Modeling
분야	Education	Education
계열	Regression model	Regression model
기원 연도	1987	2002
창시자	Anthony Bryk & Stephen Raudenbush; Judith Singer & John Willett	Stephen Raudenbush & Anthony Bryk
유형	Longitudinal multilevel model of individual change	Multilevel regression for hierarchically nested educational data
원전	Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press. ISBN: 9780195152968	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 9780761919049
별칭	Latent Growth Curve Modeling in Education, Multilevel Growth Models for Achievement, Individual Growth Trajectory Analysis, Learning Trajectory Modeling	Multilevel Models in Education, Students-in-Schools HLM, School Effects Multilevel Model, Random-Effects Models for Educational Data
관련	4	4
요약	Educational growth curve modeling is a longitudinal multilevel technique for describing and explaining how individual students change over time on an outcome such as reading or mathematics achievement. Building on the hierarchical linear models framework formalized by Bryk and Raudenbush (1987) and the applied longitudinal treatment of Singer and Willett (2003), it fits each student a personal trajectory — an intercept and one or more slopes — and then models how those personal growth parameters vary across students and relate to learner characteristics, classrooms, and schools.	Educational hierarchical linear modeling (HLM) is a multilevel regression framework for data in which students are nested within classrooms and classrooms within schools. Formalized for education by Raudenbush and Bryk, it lets the intercept and slopes of a student-level regression vary across schools, simultaneously estimating student-level relationships, school-level relationships, and the cross-level interactions between them — while producing correct standard errors that single-level regression on clustered data cannot.