Cognitive Diagnosis Models

Traditional assessments measure either a student's overall ability or diagnose specific misconceptions — rarely both. This paper proposes the Generalized Dual-Purpose Model (GDPM), which simultaneously estimates a continuous latent ability (θ) and classifies discrete misconception profiles from ordinary binary item responses.

The key insight is that misconceptions shift an examinee's item characteristic curve downward: a student holding a misconception scores systematically lower on relevant items at the same ability level, creating a detectable signal that the model exploits. Two variants are proposed — the AM-GDPM, where each misconception profile has its own ICC, and the DM-GDPM, which collapses profiles for parsimony.

Findings: Simulation studies confirm the model accurately recovers both ability and misconception profiles. Application to science assessment data identified distinct misconception patterns that ability scores alone would miss.

In low-stakes assessments, some examinees disengage — skipping items or rapid-guessing without reading — which contaminates cognitive diagnostic scores. Standard CDMs cannot distinguish a wrong answer due to skill deficiency from one due to disengagement, leading to biased attribute classifications.

This paper embeds a hierarchical response-decision process directly into the CDM. Each response is first classified by a latent engagement node (E): non-response (NA), rapid guessing (G), or genuine solution attempt (A). Only solution-behavior responses feed into the diagnostic component, cleanly separating measurement from motivation.

Findings: The model substantially reduces classification error compared to ignoring disengagement, and correctly recovers attribute mastery profiles in both simulations and a real large-scale assessment dataset.