Compare methods

	Vertical Scaling	Item Response Theory
Field	Education	Psychometrics
Family	Latent structure	Latent structure
Year of origin	2014	1952–1968
Originator	Educational measurement tradition (Thurstone; Kolen & Brennan synthesis)	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Type	Construction of a single developmental score scale spanning multiple grades	Probabilistic measurement model
Seminal source	Kolen, M. J., & Brennan, R. L. (2014). Test Equating, Scaling, and Linking: Methods and Practices (3rd ed.). Springer. ISBN: 9781493903160	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Aliases	Developmental Scaling, Vertical Linking, Cross-Grade Scaling, Growth Scale Construction	IRT, latent trait theory, item characteristic curve theory, modern test theory
Related	4	5
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.	Item response theory models the probability that a respondent answers an item correctly (or endorses it) as a function of the respondent's latent trait level and the item's own statistical properties — difficulty, discrimination, and guessing. Unlike classical test theory, IRT places persons and items on the same scale, yielding measurement that is sample-independent for items and test-independent for persons.