The application of minimum discrepancy estimation in implementation of cognitive diagnostic models

Abstract

There has been an increasing interest in implementing cognitive diagnostic models (CDMs) in operational assessments among researchers and practitioners. Operational CDMs require accurate and efficient parameter estimations. In this paper, we introduce two parameter estimation methods—the minimum discrepancy (MD) and the minimum discrepancy maximum likelihood (MDML)—in the context of CDMs. Both methods were proposed in the knowledge space theory, but have not been applied to CDMs. We then compare the performance of the two methods with the other three estimation methods used in CDMs—the joint maximum likelihood estimation (JMLE), the marginal maximum likelihood estimation (MMLE) via the expectation–maximization, and the Markov Chain Monte Carlo (MCMC) approach with Gibbs Sampling—on parameter estimation accuracy and efficiency. Results indicate the potential of applying MD and MDML in CDM parameter estimations, especially when the sample size is small. Practical applications with respect to the selection of a method among MD, MDML, MMLE, JMLE, and MCMC for specific purposes and conditions are also provided.