Jingchen Liu, Gongjun Xu and Zhiliang Ying
Data-Driven Learning of Q-Matrix
Applied Psychological Measurement 2012 36: 548 originally published online 16 August 2012
This article proposes a data-driven approach to identification of the Q-matrix and estimation of related model parameters. They introduce an estimator of the Q-matrix under the setting of the DINA model. The proposed estimator only uses the information of dependence structure of the responses (to items) and does not rely on information about the attribute distribution, or the slipping, or guessing parameters. The T-matrix serves as a connection between the observed response distribution and the model structure is another representation of the Q-matrix
Simulation studies are presented to demonstrate usefulness and applicability of the proposed method. The data from the DINA model are generated under different settings and the estimated Q-matrix and the true Q-matrix are compared.
The attributes: uniform distribution pa =2-K
si = gi =0.2
N = 500, 1,000, 2,000, and 4,000,
Data sets=100
The results show that the estimator performs well when the sample size is reasonably large. The more correlated the attributes are, the more difficult it is to estimate a Q-matrix. More ‘‘1’’s VJ contains, the more difficult it is to estimate VJ .
Comments:
It is really an interesting paper which uses our familiar knowledge to construct new things. I am puzzled about the process from formula (8) to (10)? The Q in (8) is the same to Q’, however the T is different. If so, the same Q can have many different T-matrix. Then how can we decide to use which T is right? The S function can be used to compare. If the k is too many, the Q matrix combination will be very complicated, will the computer do such burden computation?