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Variational Estimation for Multidimensional Generalized Partial Credit Model

Author

Listed:
  • Chengyu Cui

    (University of Michigan)

  • Chun Wang

    (University of Washington)

  • Gongjun Xu

    (University of Michigan)

Abstract

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model. The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.

Suggested Citation

  • Chengyu Cui & Chun Wang & Gongjun Xu, 2024. "Variational Estimation for Multidimensional Generalized Partial Credit Model," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 929-957, September.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:3:d:10.1007_s11336-024-09955-8
    DOI: 10.1007/s11336-024-09955-8
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    References listed on IDEAS

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    1. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    2. 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.
    3. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    4. Michael O. Martin & Ina V.S. Mullis, 2019. "TIMSS 2015: Illustrating Advancements in Large-Scale International Assessments," Journal of Educational and Behavioral Statistics, , vol. 44(6), pages 752-781, December.
    5. 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).
    6. Frank Rijmen & Minjeong Jeon, 2013. "Fitting an item response theory model with random item effects across groups by a variational approximation method," Annals of Operations Research, Springer, vol. 206(1), pages 647-662, July.
    7. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    8. Motonori Oka & Kensuke Okada, 2023. "Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 302-331, March.
    9. Frank Rijmen & Minjeong Jeon, 2013. "Erratum to: Fitting an item response theory model with random item effects across groups by a variational approximation," Annals of Operations Research, Springer, vol. 206(1), pages 663-663, July.
    10. 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.
    11. Silvia Cagnone & Paola Monari, 2013. "Latent variable models for ordinal data by using the adaptive quadrature approximation," Computational Statistics, Springer, vol. 28(2), pages 597-619, April.
    12. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    13. Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 37-52, March.
    14. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    15. 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.
    16. 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.
    17. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 973-995, December.
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