de la Torre, J. (2009). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34 , 115-130.
Cognitive diagnosis has become increasingly popular in recent years. It gives the examinees’ profile which includes diagnostic information related to students’ learning status; that is, it indicates which attribute (skill or task) every examinee has or has not mastered. In contrast to a summative score that is provided by the traditional item response theory models, a profile of individual attributes is obtained from cognitive diagnostic models (CDMs). The profiles provided by the CDMs include rich information to help in conducting instruction or improving students’ learning.
However, two major limitations cause the CDMs has underutilized are: first, unfamiliarity, compared to the traditional item response theory, the CDMs are relatively novel; such as the DINA model, the NIDA model, and the fusion model. Second, there is lack of commercially available software for data analysis. The purpose of this paper is that considering the DINA model to demonstrate how model parameters can be estimated by expectation-maximization (EM) algorithms.
Two model parameter estimation methods were described, the joint maximum likelihood estimation (JMLE) and the marginalized maximum likelihood estimation (MMLE). The drawback of the JMLE is that it will obtain inconsistent model parameters. The MMLE can be obtained by the EM algorithm.
The simulation results show that model parameters estimation can be recovered by using the EM algorithm. Future study lines are:
(1) the number of estimation parameters will become larger when the number of attributes is relatively large when using the EM algorithm. It will cause the computation burden, thus reducing the number of estimation parameters is needed.
(2) update the distribution for p( α ) in each iteration to more closely reflect the characteristics of the observed data.
(3) other components of the CDMs need to take into account when implementing the CDMs, such as the attribute pattern identifiability, the Q-matrix, and the estimation method for classification, et al.
The major contribution of this paper is that shows the steps of the EM algorithm for parameter estimation based on a simple CDMs when lacking of commercially available software. Following the steps, other CDMs can easy implement to the EM algorithm for parameter estimation.