An Application of the Support Vector Machine for Attribute-By-Attribute Classification in Cognitive Diagnosis

Abstract

Cognitive diagnostic modeling in educational measurement has attracted much attention from researchers in recent years. Its applications in real-world assessments, however, have been lagging behind its theoretical development. Reasons include but are not limited to requirement of large sample size, computational complexity, and lack of model fit. In this article, the authors propose to use the support vector machine (SVM), a popular supervised learning method to make classification decisions on each attribute (i.e., if the student masters the attribute or not), given a training dataset. By using the SVM, the problem of fitting and calibrating a cognitive diagnostic model (CDM) is converted into a quadratic optimization problem in hyperdimensional space. A classification boundary is obtained from the training dataset and applied to new test takers. The present simulation study considers the training sample size, the error rate in the training sample, the underlying CDM, as well as the structural parameters in the underlying CDM. Results indicate that by using the SVM, classification accuracy rates are comparable with those obtained from previous studies at both the attribute and pattern levels with much smaller sample sizes. The method is also computationally efficient. It therefore has great promise to increase the usability of cognitive diagnostic modeling in educational assessments, particularly small-scale testing programs.