Cluster Analysis for Cognitive Diagnosis: Theory and Applications

• Published in: Psychometrika Vol. 74; no. 4; pp. 633 - 665
• Main Authors: Chiu, Chia-Yi, Douglas, Jeffrey A., Li, Xiaodong
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.12.2009; Springer; Springer Nature B.V
• Subjects: Assessment; Behavioral Science and Psychology; Biological and medical sciences; Cluster analysis; Clustering; Data Analysis; Discriminant analysis; Educational Testing; Fundamental and applied biological sciences. Psychology; Humanities; Identification; Item Response Theory; Language Tests; Law; Matrices; Multivariate Analysis; Probability; Psychology; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics; Psychometrics. Statistics. Methodology; Simulation; Skills; Software; Statistical Theory and Methods; Statistics for Social Sciences; Statistics. Mathematics; Test Length; Testing and Evaluation; Theories; Theory and Methods; Variables; cluster analysis; cognitive diagnosis; latent class analysis; Cluster analysis; Automatic classification; Cognitive ability; Cognition; Diagnosis; Latent class analysis
• ISSN: 0033-3123; 1860-0980
• DOI: 10.1007/s11336-009-9125-0

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.