iPost: Subscores based on MIRT methods

Reporting of Subscores Using Multidimensional Item Response Theory

Journal	Psychometrika
Publisher	Springer New York
ISSN	0033-3123 (Print) 1860-0980 (Online)
Issue	Volume 75, Number 2 / June, 2010
DOI	10.1007/s11336-010-9158-4

Shelby J. Haberman¹ and Sandip Sinharay¹ 

(1)	ETS, Princeton, NJ, USA

Received: 13 January 2009  Revised:5 November 2009  Published online: 27 March 2010

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.

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