Specification Of Q-matrix And Its Applications To Test Construction In Cognitive Diagnosis

Cognitive diagnostic assessment theory is an important part of personalized adaptive learning.Since its introduction,the theory of cognitive diagnosis has attracted much attention because of its ability to analyze and interpret examination results in detail.The development of a cognitive diagnostic test to accurately diagnose the knowledge mastery status of each type of student includes the following steps: first the specification of the test Q-matrix or feature extraction,that is,specify the knowledge points measured for each test item,and then according to item characteristics and item parameters of test items,select the appropriate items from the test Q-matrix to form a test paper.From the basic process of cognitive diagnosis,the quality of the test Q-matrix and the quality of test papers are very important for accurate diagnosis.Therefore,how to calibrate the test Q-matrix and apply it to test construction has become an important research problem in cognitive diagnosis research.Generally speaking,the specification of the test Q-matrix is jointly completed by the subject experts through discussion,but this method has the problems of high calibration cost,strong subjectivity,and inconsistent expert opinions.Researchers have proposed a large number of methods for test construction in cognitive diagnosis.However,most of these methods are based on a certain cognitive diagnosis index.There are problems such as lack of overall consideration or large amount of calculation.Therefore,cognitive diagnosis urgently needs to explore a method for more objectively estimating the test Q-matrix and a method for generating test paper with taking into account the overall information and a small amount of calculation.The first study in this paper aims to propose an improved Q-matrix calibration method based on exploratory factor analysis.Considering that in practice,the guesses and slipping(referred to as noise)of the examines on test items will affect the quality of the tetrachoric correlation coefficient used in the exploratory factor analysis method,a noise correction for the tetrachoric correlation coefficient is proposed for the specification of Q-matrix in this study.The second study proposes a new method for test construction based on the idea of maximum inter-class distance of cluster analysis.It takes the correct response probability vector(expectation of observation response vector)of each knowledge state as the class center,and considers various constraints of the test.The mixed linear programming method is applied to maximize the minimum distance between classes in order to obtain a diagnosis test with higher correct classification rate.A simulation study was conducted to examine the performance of the new Q-matrix calibration method and test construction method.The results of the first study showed that two types of noises of guessing and slipping have some adverse effects on the correct recovery rates of the Q-matrix;the exploratory factor analysis method based on the tetrachoric correlation coefficient with data preprocessing can effectively improve the correct recovery rates of the Q-matrix in the case of large sample size and high noise.The results of the second study showed that the new method for test construction performs very well when the number of attributes is small.When the number of attributes increases,this advantage will be relatively reduced,but there is still a large advantage in correct classification rates for attribute patterns.