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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 review the theory and practices of IRT across two articles. In Part 1, we provide a broad range of topics such as foundations of educational measurement, basics of IRT, and applications of IRT using R. We focus particularly on the topics that the mirt package covers. These include unidimensional and multidimensional IRT models for dichotomous and polytomous items with continuous and discrete factors, confirmatory analysis and multigroup analysis in IRT, and estimation algorithms.In Part 2, on the other hand, we focus on more practical aspects of IRT, namely scoring, scaling, and equating.

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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

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