Ding Shu-liang

Application of Support Vector Machine to Cognitive Diagnosis

Support Vector Machine (SVM) is applied to the modern educational measurement’s diagnostic classification of 0,1 scoring test, and then comparisons of the classification results with some of the typical cognitive diagnostic classification are made. The results show that using SVM to cognitive diagnostic classification, which only needs a small sample for training, can ensure a high correct classification rate, while required short time to run. This advantage suggests that SVM could be employed to identify attributes behind in items to reduce the labor strength. Experiments show high precision and certain feasibility.

The Concept Lattices of Q-Matrices

FCA is applied into Q-matrix theory and modifies that Q is Boolean algebra in terms of Boolean addition, Boolean multiplication, and complement operator Tatsuoka 1991 1995. The structure of Item tree Tatsuoka 1995 is denied, and the concept lattices are constructed which is derived from Q matrix.

The judgment method of valid item and its application

Rule space model (RSM) and attribute hierarchy method (AHM) have been research focuses in cognitive diagnosis. Reduced Q-matrix (incidence matrix between attributes and items), which named Qr matrix, plays an important role in RSM and AHM. The column vector of Qr matrix should satisfy an attribute hierarchy, and the vector is called valid item. Studying attribute hierarchy, the judgment method of valid item is proposed. The method is applied to RSM and AHM, and empirical evidence showed that it performed very well.

Model-Based Methods for Test Equating Under Item Response Theory

There are some popular criteria for computing equating coefficients based on Item Response Theory(IRT), such as Stocking Lord method (SLcrit), Haebara method (Hcrit). In this paper some new equating criteria are driven, such as Logistic regression method (LRcrit) and symmetric relative entropy method (SREcrit). Some of these criteria may be specifically suitable for a corresponding IRT model. LRcrit could be used for the divided-by-total and difference polytomous models and may have simpler form than that of Hcrit and SLcrit. Especially, the series of LRcrit could not include the iteration algorithm in the computing procedure without losing the accuracy. And SREcrit could almost be applied to all of the models under IRT. The results of Monte Carlo study demonstrate that the new criteria have some advantages in test equating procedure, such as providing more accurate value of equating coefficients A,B or the initial value in the situations of using iteration algorithm. Moreover, they may be simpler in the form and in the computing procedure.

The judgment method of valid objects and its application

There is little room for doubt about Formal Concept Analysis (FCA) as a strong tool to be used in many domains, such as cognitive science, etc. Concept lattice is the basic data structure in FCA, and it is induced by contexts. A context is an incidence matrix that shows the relationship between objects and attributes. Attributes often share hierarchical relations which decide the form of objects. Based on attribute hierarchy, valid/invalid object were defined, the judgment method of valid/invalid object was developed on the relation between reachability matrix and valid objects, and valid object was explained from the perspective of graph theory. The judgment algorithm of valid object was proposed. The analysis of the algorithms also showed linear growth with respect to the number of valid objects. Mathematical models with 10 attributes were built for the algorithms by linear regression analysis.

Test Construction for Cognitive Diagnosis

Traditional test only provides a total score and computer adaptive test (CAT) not only provides examinee’s score but also estimates examinee’s ability. However, both two methods have not studied students’ knowledge states. Cognitive diagnostic assessment (CDA) is designed to measure specific knowledge structures and processing skills in students so as to provide information about their cognitive strengths and weaknesses. A good diagnostic test is one that goes beyond estimation of individuals’ overall ability levels. How to combine an attribute hierarchy and the reachability matrix with Henson and Douglas’s item selection strategy to construct an effective test for cognitive diagnosis in order to improve the accuracy is discussed in this paper. When compared to randomly constructed tests from the same item bank, classification rates are improved significantly.