Estimation of Q-matrix for DINA Model Using the Constrained Generalized DINA Framework

Estimation of Q-matrix for DINA Model Using the Constrained Generalized DINA Framework

by Huacheng Li

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The research of cognitive diagnostic models (CDMs) is becoming an important field of psychometrics. Instead of assigning one score, CDMs provide attribute profiles to indicate the mastering status of concepts or skills for the examinees. This would make the test result more informative. The implementation of many CDMs relies on the existing item-to-attribute relationship, which means that we need to know the concepts or skills each item requires. The relationships between the items and attributes could be summarized into the Q-matrix. Misspecification of the Q-matrix will lead to incorrect attribute profile. The Q-matrix can be designed by expert judgement, but it is possible that such practice can be subjective. There are previous researches about the Q-matrix estimation. This study proposes an estimation method for one of the most parsimonious CDMs, the DINA model. The method estimates the Q-matrix for DINA model by setting constraints on the generalized DINA model. In the simulation study, the results showed that the estimated Q-matrix fit better the empirical fraction subtraction data than the expert-design Q-matrix. We also show that the proposed method may still be applicable when the constraints were relaxed.

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