3V-JMLE: a three-valued score matrix-based joint parameter estimation algorithm in computerised adaptive testing

Abstract

During the development of a Computerised Adaptive Testing (CAT) system, certain inadequacies were found in the popular Joint Maximum Likelihood Estimation (JMLE) algorithm utilised to acquire the ideal binary score matrix. When we attempted to acquire a question-response matrix from a traditional online test item pool system, more than 90% response elements were NA in the matrix. An ideal binary score matrix could scarcely be derived from it. Thus, we proposed a revised algorithm named three-valued JMLE (3V-JMLE) in this paper. When the response could not generate an ideal binary score matrix, we can transform the non-ideal binary matrix into a three-valued score matrix, and the parameters can be estimated simply by using 3V-JMLE. Experiment results show that 3V-JMLE has the same estimation accuracy and computational efficiency as JMLE. In addition, 3V-JMLE has an extensive range of applications and high testing efficiency.