IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v35y2010i3p307-335.html
   My bibliography  Save this article

Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis

Author

Listed:
  • Li Cai

Abstract

Item factor analysis (IFA), already well established in educational measurement, is increasingly applied to psychological measurement in research settings. However, high-dimensional confirmatory IFA remains a numerical challenge. The current research extends the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm, initially proposed for exploratory IFA, to the case of maximum likelihood estimation under user-defined linear restrictions for confirmatory IFA. MH-RM naturally integrates concepts such as the missing data formulation, data augmentation, the Metropolis algorithm, and stochastic approximation. In a limited simulation study, the accuracy of the MH-RM algorithm is checked against the standard Bock-Aitkin expectation-maximization (EM) algorithm. To demonstrate the efficiency and flexibility of the MH-RM algorithm, it is applied to the IFA of real data from pediatric quality-of-life (QOL) research in comparison with adaptive quadrature-based EM algorithm. The particular data set required a confirmatory item factor model with eight factors and a variety of equality and fixing constraints to implement the hypothesized factor pattern. MH-RM converged in less than 3 minutes to the maximum likelihood solution while the EM algorithm spent well over 4 hourrs.

Suggested Citation

  • Li Cai, 2010. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 307-335, June.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:3:p:307-335
    DOI: 10.3102/1076998609353115
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998609353115
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998609353115?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    4. 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.
    5. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    6. Lehman, Anthony F., 1988. "A quality of life interview for the chronically mentally ill," Evaluation and Program Planning, Elsevier, vol. 11(1), pages 51-62, January.
    7. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    8. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Siliang Zhang & Yunxiao Chen, 2022. "Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1473-1502, December.
    2. Cosimo Magazzino & Marco Mele, 2022. "A Dynamic Factor and Neural Networks Analysis of the Co-movement of Public Revenues in the EMU," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 8(2), pages 289-338, July.
    3. Mohamed Aboraya & Haitham M. Yousof & G.G. Hamedani & Mohamed Ibrahim, 2020. "A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods," Mathematics, MDPI, vol. 8(10), pages 1-25, September.
    4. Zhang, Siliang & Chen, Yunxiao, 2022. "Computation for latent variable model estimation: a unified stochastic proximal framework," LSE Research Online Documents on Economics 114489, London School of Economics and Political Science, LSE Library.
    5. Harold Doran, 2023. "A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 37-69, February.
    6. 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.
    7. Giannelis, Alexandros & Willoughby, Emily A. & Corley, Robin & Hopfer, Christian & Hewitt, John K. & Iacono, William G. & Anderson, Jacob & Rustichini, Aldo & Vrieze, Scott I. & McGue, Matt & Lee, Jam, 2023. "The association between saving disposition and financial distress: A genetically informed approach," Journal of Economic Psychology, Elsevier, vol. 96(C).
    8. Andrej Srakar & Miroslav Verbic & Vesna Copic, 2015. "European Cultural Models in Statistical Perspective: A High-dimensionally Adjusted Cultural Index for the EU Countries, 2005-2009," ACEI Working Paper Series AWP-06-2015, Association for Cultural Economics International, revised Jul 2015.
    9. Ji Seung Yang & Li Cai, 2014. "Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis–Hastings Robbins–Monro Algorithm," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 550-582, December.
    10. Heon-Jae Jeong & Hsun-Hsiang Liao & Su Ha Han & Wui-Chiang Lee, 2020. "An Application of Item Response Theory to Scoring Patient Safety Culture Survey Data," IJERPH, MDPI, vol. 17(3), pages 1-10, January.
    11. John B. Holmes & Matthew R. Schofield & Richard J. Barker, 2022. "Pólya‐gamma data augmentation and latent variable models for multivariate binomial data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 194-218, January.
    12. Andrea Svicher & Letizia Palazzeschi & Alessio Gori & Annamaria Di Fabio, 2022. "The Gratitude Resentment and Appreciation Test-Revised Short (GRAT-RS): A Multidimensional Item Response Theory Analysis in Italian Workers," IJERPH, MDPI, vol. 19(24), pages 1-10, December.
    13. Andersson, Björn & Jin, Shaobo & Zhang, Maoxin, 2023. "Fast estimation of multiple group generalized linear latent variable models for categorical observed variables," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gregory Camilli & Jean-Paul Fox, 2015. "An Aggregate IRT Procedure for Exploratory Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 377-401, August.
    2. 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.
    3. 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.
    4. Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 581-612, December.
    5. Battauz, Michela & Vidoni, Paolo, 2022. "A likelihood-based boosting algorithm for factor analysis models with binary data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    6. Scott Monroe, 2019. "Estimation of Expected Fisher Information for IRT Models," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 431-447, August.
    7. 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.
    8. 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.
    9. 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.
    10. Yang Liu, 2020. "A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 439-468, June.
    11. Sijia Huang & Li Cai, 2021. "Lord–Wingersky Algorithm Version 2.5 with Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 973-993, December.
    12. An, Xinming & Bentler, Peter M., 2012. "Efficient direct sampling MCEM algorithm for latent variable models with binary responses," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 231-244.
    13. Wu, Jianmin & Bentler, Peter M., 2013. "Limited information estimation in binary factor analysis: A review and extension," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 392-403.
    14. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    15. Paul A. Jewsbury & Peter W. van Rijn, 2020. "IRT and MIRT Models for Item Parameter Estimation With Multidimensional Multistage Tests," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 383-402, August.
    16. Li Cai, 2015. "Lord–Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 535-559, June.
    17. Zhehan Jiang & Jonathan Templin, 2019. "Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 358-374, June.
    18. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.
    19. Nuo Xi & Michael W. Browne, 2014. "Contributions to the Underlying Bivariate Normal Method for Factor Analyzing Ordinal Data," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 583-611, December.
    20. Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:jedbes:v:35:y:2010:i:3:p:307-335. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.