A Deterministic Learning Algorithm Estimating the Q-Matrix for Cognitive Diagnosis Models

Meng-Ta Chung and Shui-Lien Chen
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Meng-Ta Chung: Department of Management Sciences, Tamkang University, New Taipei City 251301, Taiwan
Shui-Lien Chen: Department of Management Sciences, Tamkang University, New Taipei City 251301, Taiwan

Mathematics, 2021, vol. 9, issue 23, 1-11

Abstract: The goal of an exam in cognitive diagnostic assessment is to uncover whether an examinee has mastered certain attributes. Different cognitive diagnosis models (CDMs) have been developed for this purpose. The core of these CDMs is the Q-matrix, which is an item-to-attribute mapping, traditionally designed by domain experts. An expert designed Q-matrix is not without issues. For example, domain experts might neglect some attributes or have different opinions about the inclusion of some entries in the Q-matrix. It is therefore of practical importance to develop an automated method to estimate the Q-matrix. This research proposes a deterministic learning algorithm for estimating the Q-matrix. To obtain a sensible binary Q-matrix, a dichotomizing method is also devised. Results from the simulation study shows that the proposed method for estimating the Q-matrix is useful. The empirical study analyzes the ECPE data. The estimated Q-matrix is compared with the expert-designed one. All analyses in this research are carried out in R.

Keywords: Q-matrix; DINA; RRUM; CDM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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