ISSN 0439-755X
CN 11-1911/B

Acta Psychologica Sinica ›› 2020, Vol. 52 ›› Issue (1): 93-106.

• Reports of Empirical Studies •

### A method of Q-matrix validation for polytomous response cognitive diagnosis model based on relative fit statistics

WANG Daxun1,GAO Xuliang2,CAI Yan1,TU Dongbo1()

1. 1 School of Psychology, Jiangxi Normal University, Nanchang 330022, China
2 School of Psychology, Guizhou Normal University, Guiyang 550000, China
First, the reduced Q-matrix is represented by${{Q}_{r}}$, which represents a set of potential q-vectors and contains ${{2}^{K}}-1$ possible q-vectors when attributes are independent. When validating the q-vector of the first category of item j, all possible q-vectors in${{Q}_{r}}$can be used as the q-vector of the first category of item j, and the Q-matrix of remaining items remains intact. From this, the item parameters and the attribute patterns of students can be estimated, and the -2LL, AIC, and BIC can be calculated accordingly. The q-vector with the largest likelihood (or smallest AIC/BIC) is regarded as the q-vector of the first category of item j. The q-vector of the next category of the item j can also be obtained in the same way. The algorithm stops when the validated Q-matrix is same as the previous Q-matrix, or every item has been reached. In order to improve the efficiency of the method, a sequential search algorithm was proposed.