手法を比較

	Vertical Scaling	Educational Growth Curve Modeling
分野	Education	Education
系統	Latent structure	Regression model
提唱年	2014	1987
提唱者	Educational measurement tradition (Thurstone; Kolen & Brennan synthesis)	Anthony Bryk & Stephen Raudenbush; Judith Singer & John Willett
種類	Construction of a single developmental score scale spanning multiple grades	Longitudinal multilevel model of individual change
原典	Kolen, M. J., & Brennan, R. L. (2014). Test Equating, Scaling, and Linking: Methods and Practices (3rd ed.). Springer. ISBN: 9781493903160	Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press. ISBN: 9780195152968
別名	Developmental Scaling, Vertical Linking, Cross-Grade Scaling, Growth Scale Construction	Latent Growth Curve Modeling in Education, Multilevel Growth Models for Achievement, Individual Growth Trajectory Analysis, Learning Trajectory Modeling
関連	4	4
概要	Vertical scaling places tests written for different grade levels onto a single continuous score scale so that growth from one grade to the next can be measured in common units. Unlike horizontal equating, which links alternate forms intended to be interchangeable, vertical scaling deliberately links tests of differing difficulty and content to build a developmental continuum spanning, for example, grades 3 through 8. It is the measurement foundation that lets a fourth-grade and a fifth-grade score be subtracted to express how much a student grew.	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.