Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration
1Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, No. 19, Xin Jie Kou Wai Street, Hai Dian District, Beijing, 100875, China. pchen@bnu.edu.cn.
Abstract:
This study revisits the parameter estimation issues in multidimensional item response theory more thoroughly and investigates some computation details that have seldom been addressed previously when implementing the expectation-maximization (EM) algorithm for finite mixtures (EM-FM). Two research questions are: Should we rescale after each EM cycle or after the final EM cycle? How to adapt the supplemented EM algorithm to the EM-FM framework to estimate standard errors (SEs) of all unknown parameters? Analytic details of the methods are provided, and a comprehensive simulation study is conducted to provide supporting evidence. Results reveal that rescaling after each EM cycle accelerates convergence without affecting the calibration accuracy. Moreover, the SEs of all model parameters, including item parameters and population mixing proportions, recover well when the sample size is relatively large (e.g., 2000).
