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How Can Multivariate Item Response Theory Be Used in Reporting of Subscores? IRT MIRT 2PL

Haberman, Shelby J.; Sinharay, Sandip
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Item Response Theory (IRT), Multidimensional Item Response Theory (MIRT), Subscores, 2-Parameter Logistic (2PL) Model, Mean-Squared Error, Augmented Subscore


Recently, there has been increasing interest in reporting diagnostic scores. This paper examines reporting of subscores using multidimensional item response theory (MIRT) models. An MIRT model is fitted using a stabilized Newton-Raphson algorithm (Haberman, 1974, 1988) with adaptive Gauss-Hermite quadrature (Haberman, von Davier, & Lee, 2008). A new statistical approach is proposed to assess when subscores using the MIRT model have any added value over (a) the total score or (b) subscores based on classical test theory (Haberman, 2008; Haberman, Sinharay, & Puhan, 2006). The MIRT-based methods are applied to several operational data sets. The results show that the subscores based on MIRT are slightly more accurate than subscore estimates derived by classical test theory.

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