Q-Matrix Estimation Methods for Cognitive Diagnosis Models: Based on Partial Known Q-Matrix

Abstract

Different from the item response models that postulate a single underlying proficiency, cognitive diagnostic assessments (CDAs) can provide fine-grained diagnostic information about students’ knowledge state to aid classroom instructions. In CDAs, a Q-matrix that associates each item in a test with the cognitive skills is required to infer students’ knowledge states. In practice, the Q-matrix is typically performed by domain experts, which is certainly affected by the subjective tendency of experts and, to a large extent, may consist of some misspecifications. In addition, if the number of items increases, the expert-based Q-matrix specification will be time-consuming and costly. To address this concern, this paper proposed several approaches based on the likelihood ratio test to estimate Q-matrix with partial known Q-matrix and the response data, which can be used with a wide class of cognitive diagnosis models (CDMs). The feasibility and effectiveness of the proposed methods were evaluated by simulated data generated under various conditions and an example to real data. Results show that new methods can estimate Q-matrix correctly and outperforms the existing method in most conditions.