Cluster Analysis Approaches for Cognitive Diagnosis
by
Jeffrey Douglas
University of Illinois
Coauthors: Chia-Yi Chiu, University of Illinois

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 examinees 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 items-by-skills matrix. After summarizing the data with a particular vector of sum-scores, K-means cluster analysis or hierarchical agglomerative cluster analysis is then performed to group examinees. Consistency results are given for long tests, along with simulations comparing effects of test length and the method of clustering. An application to a language examination is provided, along with an illustration of how the methods can be implemented in practice.

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Date received: August 21, 2007