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Unidimensional Vertical Scaling in Multidimensional Space IRT EAP TCC

Carlson, James E.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Unidimensional Scaling, Vertical Scaling, Multidimensional Scaling, Dimensionality, Item Response Theory (IRT), Linking, Vertical Scaling, Item Difficulty, Item Discrimination (Tests), Simulation Studies, Expected a Posteriori (EAP), Item Parameter Estimation, Test Characteristic Curve (TCC) Linking, Calibration


In this paper, I consider a set of test items that are located in a multidimensional space, SM, but are located along a curved line in SM and can be scaled unidimensionally. Furthermore, I am demonstrating a case in which the test items are administered across 6 levels, such as occurs in K–12 assessment across 6 grade levels, and for which a unidimensional vertical scale can be developed. I am limiting my coverage to dichotomously scored items because the models are much simpler than those for polytomously scored items. However, the concepts discussed can be extended to the latter type of item. I also limit my demonstrations to a 2-dimensional space, S2, so I can geometrically represent my points in a 2-dimensional representation in this article. These concepts can also be extended to a higher-dimensional case.

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