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A Unified Approach to IRT Scale Linking and Scale Transformation NEAT IRT

Author(s):
von Davier, Matthias; von Davier, Alina A.
Publication Year:
2004
Report Number:
RR-04-09
Source:
ETS Research Report
Document Type:
Report
Page Count:
21
Subject/Key Words:
Item Response Models, Scale Transformation, Test Linking, Non-Equivalent-Groups Anchor Test (NEAT) Design, Nonlinear Restrictions, Maximization Procedures, Lagrange Multipliers, Item Response Theory (IRT)

Abstract

This paper examines item response theory (IRT) scale transformations and IRT scale linking methods used in the Non-Equivalent Groups with Anchor Test (NEAT) design to equate two tests, X and Y. It proposes a unifying approach to the commonly used IRT linking methods: mean-mean, mean-var linking, concurrent calibration, Stocking and Lord and Haebara characteristic curves approaches, and fixed-item parameters scale linkage. The main idea is to view any linking procedure as a restriction on the item parameter space. Then a rewriting of the log-likelihood function together with an appropriately implemented maximization procedure of the log-likelihood function under linear (or nonlinear restrictions) will accomplish the linking. The proposed method is general enough to cover both the dichotomous item response models (the one parameter logistic (1PL) model, 2PL, and 3PL) and the polytomous unidimensional IRT models like the generalized partial credit model.

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