Consistency of Cluster Analysis for Cognitive Diagnosis: The DINO Model and the DINA Model Revisited

The Asymptotic Classification Theory of Cognitive Diagnosis (ACTCD) developed by Chiu, Douglas, and Li proved that for educational test data conforming to the Deterministic Input Noisy Output "AND" gate (DINA) model, the probability that hierarchical agglomerative cluster analysis (HACA) assigns examinees to their true proficiency classes approaches 1 as the number of test items increases. This article proves that the ACTCD also covers test data conforming to the Deterministic Input Noisy Output "OR" gate (DINO) model. It also demonstrates that an extension to the statistical framework of the ACTCD, originally developed for test data conforming to the Reduced Reparameterized Unified Model or the General Diagnostic Model (a) is valid also for both the DINA model and the DINO model and (b) substantially increases the accuracy of HACA in classifying examinees when the test data conform to either of these two models.