Recognizing Uncertainty in the Q-Matrix via a Bayesian Extension of the DINA Model
DeCarlo L. T.
In this study, uncertainty in the Q-matrix with CDMs was acknowledged. The approaches to this problem include: (1) use various Q-matrices and the fit of the model under different Q-matrices were compared, (2) use sequential search algorithm, and (3) Bayesian approach which was demonstrate in this study. Under the Bayesian approach, the parameters in the RDINA/HO-RDINA models were treated as random variables and followed Bounoulli variables.
In simulations, two contexts were simulated: the latent attributed correctly specified and not correctly specified. Under the first context, the percentage of uncertain elements was manipulated. Under the second context, the number of latent attributes was specified one more or less than the true number of latent attribute. It was found that under the first context where only elements of Q-matrix were misspecified, the Bayesian approach can recover the Q-matrix well. However, when the latent attribute was not correctly specified, the recovery is quite poor for many elements.
Questions & Comments:
1. The misspecification of the Q-matrix under the second context seems have serious consequence. However, the author did not provide good explanations about the reasons. And it seems that there was not pattern about the consequence of misspecification.
2. In practice, the number of latent attribute is unknown. Thus, one have to try Q-matrices with different number of latent attributes. The efficiency of Bayesian approach is of interest, compared to other approach.
3. Can one use purification procedure to find the clean Q-matrices?