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Cluster Analysis for Cognitive Diagnosis: Theory and Applications

Published online by Cambridge University Press:  01 January 2025

Chia-Yi Chiu ,
Jeffrey A. Douglas  and
Xiaodong Li
Chia-Yi Chiu
Affiliation:
Rutgers, The State University of New Jersey
Jeffrey A. Douglas*
Affiliation:
University of Illinois
Xiaodong Li
Affiliation:
Merck & Company, Inc.
*
Requests for reprints should be sent to Jeffrey A. Douglas, 101 Illini Hall, 725 S. Wright St., Champaign, IL 61820, USA. E-mail: [email protected]
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Abstract

Latent class models for cognitive diagnosis often begin with specification of a matrix that indicates which attributes or skills are needed for each item. Then by imposing restrictions that take this into account, along with a theory governing how subjects interact with items, parametric formulations of item response functions are derived and fitted. Cluster analysis provides an alternative approach that does not require specifying an item response model, but does require an item-by-attribute matrix. After summarizing the data with a particular vector of sum-scores, K-means cluster analysis or hierarchical agglomerative cluster analysis can be applied with the purpose of clustering subjects who possess the same skills. Asymptotic classification accuracy results are given, along with simulations comparing effects of test length and method of clustering. An application to a language examination is provided to illustrate how the methods can be implemented in practice.

Keywords

cluster analysiscognitive diagnosislatent class analysis
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 4 , December 2009 , pp. 633 - 665
Copyright
Copyright © 2009 The Psychometric Society

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Footnotes

We would like to thank the English Language Institute at the University of Michigan for data and the National Science Foundation for funding (grant number 0648882).

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