Cluster analysis for cognitive diagnosis: Theory and applications

Chia Yi Chiu, Jeffrey A. Douglas, Xiaodong Li

Research output: Contribution to journalArticlepeer-review

155 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)633-665
Number of pages33
Issue number4
StatePublished - Dec 2009
Externally publishedYes

Bibliographical note

Funding Information:
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). Requests for reprints should be sent to Jeffrey A. Douglas, 101 Illini Hall, 725 S. Wright St., Champaign, IL 61820, USA. E-mail:


  • Cluster analysis
  • Cognitive diagnosis
  • Latent class analysis


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