Methodological tutorial demonstrates a unified item and testlet response framework in psychometrics, highlighting enhanced calibration and equating capabilities.
Item response theory (IRT) and testlet response theory (TRT) are foundational psychometric frameworks for modeling the relationship between latent traits and observed item responses. Although several R packages support standard IRT estimation, few provide integrated support for testlet models, joint IRT–TRT calibration, and ancillary functions needed in operational testing programs. This paper introduces tirt, a R package that offers a unified estimation framework spanning multidimensional IRT models (Rasch, 2PL, 3PL, GRM, GPCM, PCM) and a broad family of testlet response theory models (Rasch Testlet, 2PL Testlet, 3PL Testlet, Bifactor, GR Testlet, PCM Testlet). The package additionally provides functions for data simulation, fixed-parameter calibration, equating, and a unique joint IRT–TRT estimation. We present the theoretical foundations, describe the estimation algorithms, and illustrate major functions with both simulated and real-data examples. The package is designed for researchers, graduate students, and practitioners in educational measurement, psychology, and the health professions.
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Xiong et al. (2026) studied this question.
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