Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model

Chia Yi Chiu, Hans Friedrich Koehn

Research output: Contribution to journalArticle

Abstract

The asymptotic classification theory of cognitive diagnosis (ACTCD) provided the theoretical foundation for using clustering methods that do not rely on a parametric statistical model for assigning examinees to proficiency classes. Like general diagnostic classification models, clustering methods can be useful in situations where the true diagnostic classification model (DCM) underlying the data is unknown and possibly misspecified, or the items of a test conform to a mix of multiple DCMs. Clustering methods can also be an option when fitting advanced and complex DCMs encounters computational difficulties. These can range from the use of excessive CPU times to plain computational infeasibility. However, the propositions of the ACTCD have only been proven for the Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model. For other DCMs, there does not exist a theoretical justification to use clustering for assigning examinees to proficiency classes. But if clustering is to be used legitimately, then the ACTCD must cover a larger number of DCMs than just the DINA model and the DINO model. Thus, the purpose of this article is to prove the theoretical propositions of the ACTCD for two other important DCMs, the Reduced Reparameterized Unified Model and the General Diagnostic Model.

Original languageEnglish (US)
Pages (from-to)585-610
Number of pages26
JournalPsychometrika
Volume81
Issue number3
DOIs
StatePublished - Sep 1 2016

Fingerprint

Model Diagnostics
Cluster analysis
Cluster Analysis
Clustering Methods
Proposition
Output
Model
Diagnostics
Clustering
Statistical Models
Infeasibility
CPU Time
Parametric Model
Justification
Statistical Model
Program processors
Cover
Unknown

Keywords

  • Reduced Reparameterized Unified Model (Reduced RUM)
  • cluster analysis
  • cognitive diagnosis
  • consistency
  • diagnostic classification model
  • general diagnostic classification models
  • general diagnostic model (GDM)

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

Cite this

Consistency of Cluster Analysis for Cognitive Diagnosis : The Reduced Reparameterized Unified Model and the General Diagnostic Model. / Chiu, Chia Yi; Koehn, Hans Friedrich.

In: Psychometrika, Vol. 81, No. 3, 01.09.2016, p. 585-610.

Research output: Contribution to journalArticle

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