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Parameter Estimation of the Reduced RUM Using the EM Algorithm

Diagnostic classification models (DCMs) are psychometric models widely discussed by researchers nowadays because of their promising feature of obtaining detailed information on students’ mastery on specific attributes. Model estimation is essential for further implementation of these models, and estimation methods are often developed within some general framework, such as generalized diagnostic model (GDM) of von Davier, the log-linear diagnostic classification model (LDCM), and the generalized deterministic input, noisy-and-gate (G-DINA). Using a maximum likelihood estimation algorithm, this article addresses the estimation issue of a complex compensatory DCM, the reduced reparameterized unified model (rRUM), whose estimation under general frameworks could be lengthy due to the complexity of the model. The proposed estimation method is demonstrated on simulated data as well as a real data set, and is shown to provide accurate item parameter estimates for the rRUM.