Abstract
Stable maximum likelihood estimation (MLE) of item parameters in 3PLM with a modest sample size remains a challenge. The current study presents a mixture-modeling approach to 3PLM based on which a feasible Expectation-Maximization-Maximization (EMM) MLE algorithm is proposed. The simulation study indicates that EMM is comparable to the Bayesian EM in terms of bias and RMSE. EMM also produces smaller standard errors (SEs) than MMLE/EM. In order to further demonstrate the feasibility, the method has also been applied to two real-world data sets. The point estimates in EMM are close to those from the commercial programs, BILOG-MG and flexMIRT, but the SEs are smaller.
Highlights
In the field of educational measurement, item response theory (IRT) models are a powerful tool aimed at providing an appropriate representation of students’ test-taking behavior, and produce accurate estimates of students’ ability
EMM can be considered as a modified version of the maximum likelihood estimation via expectation-maximization (MMLE/EM) algorithm (Bock and Aitkin, 1981) and the extra maximization step is especially designed for the guessing parameter due to a different setup for the complete data based on a mixture-modeling reformulation of the 3PLM
Especially the work by von Davier (2009) and Hutchinson (1991), the current study presents a new mixture-modeling reformulation of the 3PLM by introducing an extra latent indicator for the guessing behavior and develops a feasible maximum likelihood estimation (MLE) algorithm, this concept of mixture-modeling approach for the 3PLM has recurred in the IRT literature
Summary
In the field of educational measurement, item response theory (IRT) models are a powerful tool aimed at providing an appropriate representation of students’ test-taking behavior, and produce accurate estimates of students’ ability. EMM can be considered as a modified version of the MMLE/EM algorithm (Bock and Aitkin, 1981) and the extra maximization step is especially designed for the guessing parameter due to a different setup for the complete data based on a mixture-modeling reformulation of the 3PLM. This mixture-modeling approach to the 3PLM is not entirely new in the IRT literature. The last section gives a brief discussion and future directions
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