The Development And Application Of Based Two-stage Estimation Method Of Q-matrix For Cognitive Diagnosis Test

Cognitive diagnosis theory shows the huge development potential in the field of educational and psychological evaluation, depended on its advantage of the accurate assessment of the participants from microcosmic and cognitive angle. However, it is necessary to ensure the rationality of the constructed test Q-matrix before taking these advantages. In most cases, the Q-matrix is constructed from the judgments of experts in the educational domain, which has a disadvantage—whether experts have the same level and the unified opinion will seriously affects the correctness of the test Q-matrix. It is widely recognized that a misspecification of the Q-matrix can negatively affect the estimation of the model parameters, which may then result in the misclassification of examinees. In order to overcome this problem and help expert decision, many foreign researchers have developed six kinds of methods which are based examines’ responses data with data-driven perspective.Based on the advantages and disadvantages of Nonlinear Penalized Estimation method and Bayesian extension method, this article proposes a new method. The advantage of Nonlinear Penalized Estimation is that it does not need to define the primary test Q-matrix by expert, and the disadvantage is that the improper selection for objective function estimation and too absolute cut-off point lead to make a mistake. The advantage of Bayesian extension method is that it can effectively estimate Q matrix but it must be known that Q matrix elements be defined as the premise. Because Nonlinear Penalized Estimation method is improper selection of defects, this paper puts forward the modified of Nonlinear Penalized Estimation method; In order to overcome Nonlinear Penalized Estimation method and Bayesian extension method’s shortcoming, this paper proposes an Two-Stage Estimation method. In order to prove the improvement effect of the Modified Nonlinear Penalized Estimation method and Two-Stage Estimation method, This study uses monte carlo simulation to compare the MMR of Nonlinear Penalized Estimation method, modified Nonlinear Penalized Estimation method and Two-Stage Estimation method in the number of participants, test length, number of attributes, and cut-off point selection criteria. Tatsuoka’s subtraction of fractions data is also used to discuss the performance of these methods. The findings showed:1) The Modified Nonlinear Penalized Estimation method works better than Nonlinear Penalized Estimation method not only on the estimation efficiency but also on the estimation accuracy; Compares to Nonlinear Penalized Estimation method and the Modified Nonlinear Penalized Estimation method, Two-Stage Estimation method can effectively improve the accuracy of the test Q matrix estimation.2) With the increasing number of attributes, Nonlinear Penalized Estimation method, Modified Nonlinear Penalized Estimation method and Two-Stage Estimation method’s estimation accuracy are all dropped. But three methods of drop are different, Nonlinear Penalized Estimation method is the largest of all.3) Nonlinear Penalized Estimation method’ estimation accuracy is in contrast with the Modified Nonlinear Penalized Estimation method and Two-Stage Estimation method on the test length. The Modified Nonlinear Penalized Estimation method and Two-Stage Estimation method work better than Nonlinear Penalized Estimation method.4) Two-Stage Estimation method works better, when cut-off point is 0.7/0.3 or 0.6/0.4. If the number of participants are small, cut-off point is 0.6/0.4 more suitable.5) These method’s performance on Tatsuoka’s subtraction of fractions data confirmed the conclusion of simulation studies.