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A Metropolis–Hastings Robbins–Monro algorithm via variational inference for estimating the multidimensional graded response model: a calculationally efficient estimation scheme to deal with complex test structures

Author

Listed:
  • Xue Wang

    (Northeast Normal University)

  • Jing Lu

    (Northeast Normal University)

  • Jiwei Zhang

    (Northeast Normal University)

Abstract

This paper introduces the Metropolis–Hastings variational inference Robbins–Monro (MHVIRM) algorithm, a modification of the Metropolis–Hastings Robbins–Monro (MHRM) method, designed for estimating parameters in complex multidimensional graded response models (MGRM). By integrating a black-box variational inference (BBVI) approach, MHVIRM enhances computational efficiency and estimation accuracy, particularly for models with high-dimensional data and complex test structures. The algorithms effectiveness is demonstrated through simulations, showing improved precision over traditional MHRM, especially in scenarios with complex structures and small sample sizes. Moreover, MHVIRM is robust to initial values. The applicability is further illustrated with a real dataset analysis.

Suggested Citation

  • Xue Wang & Jing Lu & Jiwei Zhang, 2025. "A Metropolis–Hastings Robbins–Monro algorithm via variational inference for estimating the multidimensional graded response model: a calculationally efficient estimation scheme to deal with complex te," Computational Statistics, Springer, vol. 40(3), pages 1253-1284, March.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01533-x
    DOI: 10.1007/s00180-024-01533-x
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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. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    3. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    4. 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).
    5. 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.
    6. 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.
    7. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    8. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    9. J. C. Naylor & A. F. M. Smith, 1982. "Applications of a Method for the Efficient Computation of Posterior Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 214-225, November.
    10. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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