Abstract
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.