MULTILEVEL ITEM RESPONSE THEORY MODEL USING MML-GHQ METHOD FOR HIERARCHICAL DATA

DOI: https://doi.org/10.30598/barekengvol20iss4pp3259-3270
Keywords: Gauss-Hermite Quadrature, Hierarchical Data, Maximum Marginal Likelihood, Multilevel Item Response Theory

Abstract

Hierarchical item response data require a multilevel approach to capture the diversity of respondent abilities and item characteristics by separating variations between examinees and schools to make item parameter and ability estimates more precise. This study aims to develop a two-parameter logistic multilevel item response theory (MIRT 2PL) model, employing the maximum marginal likelihood method with Gauss-Hermite quadrature (MML-GHQ) to estimate the rank order of examinees’ abilities. This study specifically investigates the efficiency and accuracy of the MIRT 2PL model with MML-GHQ to predict the ability rankings of examinees. The research incorporates both simulated and empirical data. The simulation study generated item response data under a two-level hierarchical structure, where examinees were nested within schools. The population consisted of 50 schools, with 20–30 students per school and five items. Each examinee’s ability was modelled as a combination of school-level and individual-level effects, under two conditions of school variability: high (τ = 1.2) and low (τ = 0.6). Random samples were drawn from the population, and the sampling process was repeated 10 times to assess consistency. The analysis included estimating item parameters, variance components, and examinees’ abilities using the EAP approach. Model performance was evaluated using RMSE, Spearman correlation, and computation time. Results indicated that MML-GHQ produced accurate and consistent rank estimates, particularly under high school variability. Using PISA data, increasing the number of schools, students, and items in the empirical data yielded results consistent with the simulation study. In conclusion, the MIRT 2PL model with MML-GHQ offers an effective and efficient alternative for estimating ability rankings in hierarchical item response data.

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Published
2026-08-24
How to Cite
[1]
A. Dwinata, A. Kurnia, A. H. Wigena, and M. N. Aidi, “MULTILEVEL ITEM RESPONSE THEORY MODEL USING MML-GHQ METHOD FOR HIERARCHICAL DATA”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 3259-3270, Aug. 2026.
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Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
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Copyright (c) 2026 Alona Dwinata, Anang Kurnia, Aji Hamim Wigena, Muhammad Nur Aidi

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