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Item response theory and its applications in educational measurement Part II: Theory and practices of test equating in item response theory

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Tsuyoshi Yamada, Hirotaka Fukuhara, Kazuki Hori

Published Online: Dec 21 2020

DOI: 10.1002/wics.1543

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Abstract Item response theory (IRT) is a class of latent variable models, which are used to develop educational and psychological tests (e.g., standardized tests, personality tests, tests for licensure and certification). We offer readers with comprehensive overviews of the theory and applications of IRT through two articles. While Part 1 of the review discusses topics such as foundations of educational measurement, IRT models, item parameter estimation, and applications of IRT with R, this Part 2 reviews areas of test scores based on IRT. The primary focus is on presenting various topics with respect to test equating such as equating designs, IRT‐based equating methods, anchor stability check methods, and impact data analysis that psychometricians would deal with for a large‐scale standardized assessment in practice. These analyses are illustrated in Example section using data from Kolen and Brennan (2014). We also cover the foundation of IRT, IRT‐based person ability parameter estimation methods, and scaling and scale score. This article is categorized under: Applications of Computational Statistics > Psychometrics Software for Computational Statistics > Software/Statistical Software

Item characteristic curves (ICCs) with different sets of item parameters. Subplot (a) varies item discrimination (a_i = 0.5, 1.0, 2.0), subplot (b) varies item difficulty (b_i = − 1.5, 0.0, 1.5), and subplot (c) varies pseudoguessing parameter (c_i = 0.00, 0.15, 0.30). The other parameters in each subplot set at a_i = 1, b_i = 0, and c_i = 0

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Test characteristic curves (TCCs) after equating (Top) and difference in number correct across forms (bottom)

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Item characteristic curves (ICCs) for flagged Items by the D2 method

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Nonequivalent groups with anchor test design

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Equating designs

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Example of item information curves (IICs; top left), test information curve (TIC; top right), and the corresponding standard error of estimate (bottom left). Item 1: (a₁, b₁, c₁) = (1.0, 0.0, 0.0), Item 2: (a₂, b₂, c₂) = (1.0, 1.5, 0.0), Item 3: (a₃, b₃, c₃) = (1.5, − 1.5, 0.0), Item 4: (a₄, b₄, c₄) = (1.0, 0.0, 0.2)

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Three hypothetical item characteristic curves (ICCs) and the corresponding test characteristic curve

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