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Reporting of Subscores Using Multidimensional Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Shelby J. Haberman and
Sandip Sinharay
Shelby J. Haberman
Affiliation:
ETS
Sandip Sinharay*
Affiliation:
ETS
*
Requests for reprints should be sent to Sandip Sinharay, ETS, Princeton, NJ, USA. E-mail: ssinharay@ets.org
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Abstract

Recently, there has been increasing interest in reporting subscores. This paper examines reporting of subscores using multidimensional item response theory (MIRT) models (e.g., Reckase in Appl. Psychol. Meas. 21:25–36, 1997; C.R. Rao and S. Sinharay (Eds), Handbook of Statistics, vol. 26, pp. 607–642, North-Holland, Amsterdam, 2007; Beguin & Glas in Psychometrika, 66:471–488, 2001). A MIRT model is fitted using a stabilized Newton–Raphson algorithm (Haberman in The Analysis of Frequency Data, University of Chicago Press, Chicago, 1974; Sociol. Methodol. 18:193–211, 1988) with adaptive Gauss–Hermite quadrature (Haberman, von Davier, & Lee in ETS Research Rep. No. RR-08-45, ETS, Princeton, 2008). A new statistical approach is proposed to assess when subscores using the MIRT model have any added value over (i)  the total score or (ii)  subscores based on classical test theory (Haberman in J. Educ. Behav. Stat. 33:204–229, 2008; Haberman, Sinharay, & Puhan in Br. J. Math. Stat. Psychol. 62:79–95, 2008). 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.

Keywords

2PL modelMean squared erroraugmented subscore

Information

Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 2 , June 2010, pp. 209 - 227
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

Note: Any opinions expressed in this publication are those of the authors and not necessarily of Educational Testing Service.

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