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

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  • Ping Chen

    (Beijing Normal University)

  • Chun Wang

    (University of Washington)

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).

Suggested Citation

  • Ping Chen & Chun Wang, 2021. "Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 299-326, March.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:1:d:10.1007_s11336-021-09745-6
    DOI: 10.1007/s11336-021-09745-6
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    4. Chun Wang & Hua-Hua Chang, 2011. "Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 363-384, July.
    5. Michael Edwards, 2010. "A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 474-497, September.
    6. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    7. Daniel Segall, 1996. "Multidimensional adaptive testing," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 331-354, June.
    8. Lihua Yao, 2012. "Multidimensional CAT Item Selection Methods for Domain Scores and Composite Scores: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 495-523, July.
    9. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    10. Ping Chen & Chun Wang, 2016. "A New Online Calibration Method for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 674-701, September.
    11. M. Jamshidian & R. I. Jennrich, 2000. "Standard errors for EM estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 257-270.
    12. Chun Wang, 2015. "On Latent Trait Estimation in Multidimensional Compensatory Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 428-449, June.
    13. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    14. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.
    15. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
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