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

Chun Wang; Hua Hua Chang; Keith A. Boughton

doi:10.1007/s11336-010-9186-0

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

Chun Wang, Hua Hua Chang, Keith A. Boughton

Psychology (Twin Cities)

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

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.

Original language	English (US)
Pages (from-to)	13-39
Number of pages	27
Journal	Psychometrika
Volume	76
Issue number	1
DOIs	https://doi.org/10.1007/s11336-010-9186-0
State	Published - Jan 2011

Bibliographical note

Funding Information:
This study was partially supported by 2009–2010 CTB/McGraw-Hill Research and Development (R&D) Research Grant. Part of the paper was originally presented in 2009 GMAC Conference on Computerized Adaptive Testing, Minneapolis, June 2009. The authors are indebted to the editor, associate editor and two anonymous reviewers for their suggestions and comments on the earlier manuscript.

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

Keywords

Fisher information
Kullback-Leibler information
Multi-dimensional adaptive testing

Publisher link

10.1007/s11336-010-9186-0

Find It

Find It at U of M Libraries

Cite this

@article{02a736a28d0e4a96a0835cf4235474d7,

title = "Kullback-Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing",

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 = "Fisher information, Kullback-Leibler information, Multi-dimensional adaptive testing",

author = "Chun Wang and Chang, {Hua Hua} and Boughton, {Keith A.}",

note = "Funding Information: This study was partially supported by 2009–2010 CTB/McGraw-Hill Research and Development (R&D) Research Grant. Part of the paper was originally presented in 2009 GMAC Conference on Computerized Adaptive Testing, Minneapolis, June 2009. The authors are indebted to the editor, associate editor and two anonymous reviewers for their suggestions and comments on the earlier manuscript. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

year = "2011",

month = jan,

doi = "10.1007/s11336-010-9186-0",

language = "English (US)",

volume = "76",

pages = "13--39",

journal = "Psychometrika",

issn = "0033-3123",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Kullback-Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing

AU - Wang, Chun

AU - Chang, Hua Hua

AU - Boughton, Keith A.

N1 - Funding Information: This study was partially supported by 2009–2010 CTB/McGraw-Hill Research and Development (R&D) Research Grant. Part of the paper was originally presented in 2009 GMAC Conference on Computerized Adaptive Testing, Minneapolis, June 2009. The authors are indebted to the editor, associate editor and two anonymous reviewers for their suggestions and comments on the earlier manuscript. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

KW - Fisher information

KW - Kullback-Leibler information

KW - Multi-dimensional adaptive testing

UR - http://www.scopus.com/inward/record.url?scp=79952244577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952244577&partnerID=8YFLogxK

U2 - 10.1007/s11336-010-9186-0

DO - 10.1007/s11336-010-9186-0

M3 - Article

AN - SCOPUS:79952244577

SN - 0033-3123

VL - 76

SP - 13

EP - 39

JO - Psychometrika

JF - Psychometrika

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this