Q-matrix Estimation Method Of Cognitive Diagnosis Based On Attribute Definition

Cognitive diagnosis makes a scientific and accurate assessment of the student's learning process from the perspective of micro-cognition. It has played a great potential in the field of psychology and educational data mining. However, there are not many educational tests based on the theory of cognitive diagnosis. The major difficulty lies in the fact that the Q-matrix which reflects the relationship between project and attribute can't be reasonably defined. Constructing the correct Q-matrix is the key link in the practice of cognitive diagnosis. It is the fundamental difference between the cognitive diagnosis theory and the traditional measurement theory. The definition of the Q-matrix is generally done by the domain experts and the psychometric experts based on diagnostic purposes through discussion. However, there are many problems such as high cost of definition, strong subjectivity and disagreement among experts. Therefore, it is urgent to study the more objective estimation method of Q-matrix. In recent years, it has become the focus of attention of scholars at home and abroad and has developed a series of estimation methods.In order to achieve the estimation of Q-matrix, the thesis studies some classical Q-matrix estimation methods. Aiming at the shortcomings of classical Barnes hill climbing method, such as poor search ability and easy to fall into the local extremum,this paper proposes the genetic algorithm of the global optimization to improve the classic hill climbing method. This paper makes use of the DeCarlo Bayesian method of higher accuracy to optimize the estimation results. The experimental results are verifiedon the simulated data and the real data sets respectively. The difference between the new method and other methods is studied by analyzing the marginal match rate (MMR), the discrepancy distance (DD) and the model fitting index. The simulation data were generated by Xiang (2013) method. Monte Carlo simulation system was used to study the influence of the number of students, the number of attributes and the total number of items on the performance of each method. The real data comes from the classical Tatsuoka fractional subtraction and the SAT test. The experimental results verify the algorithm.A large number of experimental studies show that the estimation performance of the genetic algorithm is better than that of the Barnes climbing method and the nonlinear penalty estimation method under the same conditions. The estimated Q-matrix which is further optimized by Bayesian method is closer to the real Q-matrix, and the estimation accuracy is improved obviously.