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	Educational Growth Curve Modeling	階層線形モデリング（HLM / マルチレベルモデリング）
分野	Education	統計学
系統	Regression model	Hypothesis test
提唱年	1987	1986
提唱者	Anthony Bryk & Stephen Raudenbush; Judith Singer & John Willett	Raudenbush & Bryk (popularized); Goldstein (parallel development)
種類	Longitudinal multilevel model of individual change	Parametric nested-data regression
原典	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: 978-0761919049
別名	Latent Growth Curve Modeling in Education, Multilevel Growth Models for Achievement, Individual Growth Trajectory Analysis, Learning Trajectory Modeling	HLM, MLM, multilevel modeling, multilevel analysis
関連	4	4
概要	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.	Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (building on work from the mid-1980s), HLM simultaneously estimates individual-level and group-level effects while correctly partitioning variance across levels.