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

Wang, Chun; Chang, Hua Hua; Boughton, Keith A.

doi:10.1007/s11336-010-9186-0

Cited by 52 publications

(57 citation statements)

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“…In fact, the two-dimensional case presented in Wang et al (2011) can be seen as a special case, and hence, the conclusion given in this paper has greater universality. This derivation adds to our knowledge about the characteristics of KI in a more general case and hence helps us identify the items that are favored by KI.…”

Section: Kl Index and D-optimality Methodsmentioning

confidence: 66%

“…Suppose that there are two possible candidate items in the item bank; Item 1 has discrimination parameters a 1 = a 2 = 1.5, and Item 2 has discrimination parameters a 1 = 2, a 2 = 0. Suppose that b-parameters for both items follow the linear combinations given in Theorem 2 of Wang et al (2011). It is clear that Item 1 will be selected by KI because it has larger MDISC.…”

Section: Discussionmentioning

confidence: 99%

“…First, to characterize the behavior of KI, Wang, Chang, and Boughton (2011) presented a geometric approach to connect the item KI and the item parameters under a two-dimensional item response model. In particular, they derived that as the test length n goes to infinity, the magnitude of KI is proportional to the trace of the Fisher information (F) matrix and, consequently, proportional to the square of the item multidimensional discrimination (MDISC, Reckase & McKinley, 1991).…”

Section: Kl Index and D-optimality Methodsmentioning

confidence: 99%

“…Comparing KI with the Fisher-information-based method, we know that in the unidimensional case, maximizing KI will eventually be equivalent to maximizing the Fisher information (Chang & Ying, 1996), but this is no longer true in the two-dimensional case (Wang et al, 2011) or in higher-dimensional cases. Specifically, in the D-optimality method, by maximizing the determinant of the F matrix, it is algebraically equivalent to maximizing the product of the eigenvalues of the F matrix.…”

Section: Kl Index and D-optimality Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles

Chun

Chang

2011

Psychometrika

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Section: Kl Index and D-optimality Methodsmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

Section: Kl Index and D-optimality Methodsmentioning

confidence: 99%

Section: Kl Index and D-optimality Methodsmentioning

confidence: 99%

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Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles

Chun

Chang

2011

Psychometrika

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“…For example, our recent works presented in Psychometrika (Wang, Chang, and Boughton, 2011; were initially inspired by reading a preprint of the book. As pointed out by Prof. Reckase on page 76, "MIRT analysis is still fairly early in its development", and there are a lot of new challenges awaiting further inquiry.…”

mentioning

confidence: 99%

M.D. RECKASE (2009) Multidimensional Item Response Theory (Statistics for Social and Behavioral Sciences).

Chang

Wang

2011

Psychometrika

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The publication of Multidimensional Item Response Theory (2009), as part of Springer's Statistics for Social and Behavioral Sciences Series, adds a valuable piece to the existing resource of Item Response Theory (IRT). This book gives a comprehensive review of theories and applications in various aspects of Multidimensional Item Response Theory (MIRT). The term Multidimensional is due to the focus on multidimensional traits, contrasting to most IRT books in which the latent trait is assumed to be scalar. Actually, MIRT can be viewed as an extension of IRT for better interpreting the interaction between item characteristics and examinees' behaviors. Practitioners have been trying for decades to quantify some testing behaviors by MIRT that unidimensional IRT failed to interpret. As an example of this, Roussos and Stout (1996) used MIRT to demonstrate why DIF can happen to some items. Today researchers in the field have increasingly realized the advantage of MIRT for getting more information, such as a diagnostic profile, in addition to a single score. Many certification and admission boards are trying to combine regular tests with diagnostic services to allow candidates to obtain more informative diagnostic profiles of their abilities. Undoubtedly, MIRT provides a theoretical background for such purposes (Mulder and van der Linden, 2009).The author of the book, Professor Mark Reckase, is a distinguished scholar, practitioner, and teacher. He has made many significant contributions to test theory, particularly MIRT. The objective of the book is to provide an overview of MIRT in an accessible manner to a wide audience without sacrificing either expositional depth or clarity. To achieve this purpose, the book is divided into three parts. The first part includes Chaps. 1-3, which provides a general conceptual overview of item response modeling, a brief summary of unidimensional IRT, and a lineage of historical underpinnings of MIRT. The second part, which includes Chaps. 4-6, introduces the basic characteristics of MIRT, and focuses on mathematical formulations for different MIRT models, statistics used for describing items in MIRT, and various estimation methods. The rest of the chapters form the third part, which emphasizes the application of MIRT models. Chapter 7 describes how to determine the number of dimensions for explaining the item person interaction. Chapter 8 shows the invariance property of MIRT modeling and describes how to define and transform the coordinate system. Chapter 9 lays out the procedures for converting the results from different MIRT calibrations to a common coordinate system, which is especially useful to maintain a large-scale assessment system over years. The last chapter shows how all the procedures can be applied to a computerized adaptive testing context. This book was written by a single author and the readers will enjoy the coherence flowing through the book. Despite of MIRT's complexity, this book is well delivered in an engaging manner. Every chapter is self-contained and starts wit...

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A Study on Weighted Doubly Truncated Renyi Divergence

Moharana

Kayal

2020

Recent Advances in Intelligent Information Systems and Applied Mathematics

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

Abstract: Kullback–Leibler information, Fisher information, multi-dimensional adaptive testing,

Cited by 52 publications

References 40 publications

Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles

Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles

M.D. RECKASE (2009) Multidimensional Item Response Theory (Statistics for Social and Behavioral Sciences).

A Study on Weighted Doubly Truncated Renyi Divergence

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