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Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration

Published online by Cambridge University Press:  01 January 2025

Ping Chen Open the ORCID record for Ping Chen [Opens in a new window]  and
Chun Wang
Ping Chen*
Affiliation:
Beijing Normal University
Chun Wang
Affiliation:
University of Washington
*
Correspondence should be made to Ping Chen, Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, No. 19, Xin Jie Kou Wai Street, Hai Dian District, Beijing100875, China. Email: [email protected]
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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).

Keywords

EM algorithm for finite mixturesSupplemented EMError covariance matrixMultidimensional item response theoryRescaling schemeStandard error
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 1 , March 2021 , pp. 299 - 326
Copyright
Copyright © 2021 The Psychometric Society

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