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

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

Which one is more accurate, BILOG or R program? (a comparison for score test equating)

“…The results of the goodness of fit analysis Table 1 shows that the item analysis based on the Item Response Theory fits the 2-PL model for both packages. Then, based on the logistic parameter two (2PL), the model adds completion parameters to the difficulty level [63], [64]. Further analysis carried out to see the good or poor characteristics of the questions with the 2-PL model show the following results: package A had 27 good items and 13 poor items, while package B had 24 good item and 16 poor items.…”

Intra and Inter-Local Item Dependence of Mathematics Items

“…Test equating -LID can impact test equating, which is the process of linking scores from several forms of a test. LID may affect the comparability of scores across different test versions (Hori et al, 2022). It is typically seen for instruments composed of items or groups of items that measure various facets of the latent variable or different domains of an underlying construct.…”