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Kullback–Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing

Published online by Cambridge University Press:  01 January 2025

Chun Wang ,
Hua-Hua Chang  and
Keith A. Boughton
Chun Wang*
Affiliation:
University of Illinois at Urbana-Champaign
Hua-Hua Chang
Affiliation:
University of Illinois at Urbana-Champaign
Keith A. Boughton
Affiliation:
CTB/McGraw-Hill
*
Requests for reprints should be sent to Chun Wang, Department of Psychology, University of Illinois at Urbana-Champaign, 603 E. Daniel St., Champaign, IL 61820, USA. E-mail: cwang49@uiuc.edu
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Abstract

This paper first discusses the relationship between Kullback–Leibler information (KL) and Fisher information in the context of multi-dimensional item response theory and is further interpreted for the two-dimensional case, from a geometric perspective. This explication should allow for a better understanding of the various item selection methods in multi-dimensional adaptive tests (MAT) which are based on these two information measures. The KL information index (KI) method is then discussed and two theorems are derived to quantify the relationship between KI and item parameters. Due to the fact that most of the existing item selection algorithms for MAT bear severe computational complexity, which substantially lowers the applicability of MAT, two versions of simplified KL index (SKI), built from the analytical results, are proposed to mimic the behavior of KI, while reducing the overall computational intensity.

Keywords

Kullback–Leibler informationFisher informationmulti-dimensional adaptive testing
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 1 , January 2011 , pp. 13 - 39
Copyright
Copyright © 2010 The Psychometric Society

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