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| Vertical Scaling× | Educational Growth Curve Modeling× | |
|---|---|---|
| Field | Education | Education |
| Family≠ | Latent structure | Regression model |
| Year of origin≠ | 2014 | 1987 |
| Originator≠ | Educational measurement tradition (Thurstone; Kolen & Brennan synthesis) | Anthony Bryk & Stephen Raudenbush; Judith Singer & John Willett |
| Type≠ | Construction of a single developmental score scale spanning multiple grades | Longitudinal multilevel model of individual change |
| Seminal source≠ | 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 |
| Aliases | 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 |
| Related | 4 | 4 |
| Summary≠ | 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. |
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