方法对比

	Educational Growth Curve Modeling	生长混合模型 (GMM)
领域	Education	统计学
方法族	Regression model	Latent structure
起源年份	1987	1999
提出者	Anthony Bryk & Stephen Raudenbush; Judith Singer & John Willett	Bengt O. Muthén & Kerby Shedden
类型	Longitudinal multilevel model of individual change	Latent class / longitudinal growth model
开创性文献	Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press. ISBN: 9780195152968	Muthén, B. O. & Shedden, K. (1999). Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm. Biometrics, 55(2), 463–469.
别名	Latent Growth Curve Modeling in Education, Multilevel Growth Models for Achievement, Individual Growth Trajectory Analysis, Learning Trajectory Modeling	Büyüme Karışım Modeli (Growth Mixture Model — GMM), GMM, latent class growth analysis extension, mixture latent growth curve model
相关	4	5
摘要	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.	The Growth Mixture Model, introduced by Muthén and Shedden in 1999, is a longitudinal latent variable method that identifies distinct subpopulations — latent trajectory classes — each following its own growth curve over time. It extends the standard Latent Growth Curve (LGC) model by allowing the sample to be composed of an unknown mixture of classes with different intercepts, slopes, and variance structures.