IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v39y2014i6p550-582.html
   My bibliography  Save this article

Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis–Hastings Robbins–Monro Algorithm

Author

Listed:
  • Ji Seung Yang

    (University of Maryland)

  • Li Cai

    (University of California)

Abstract

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis–Hastings Robbins–Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard errors efficiently. Simulations, with various sampling and measurement structure conditions, were conducted to obtain information about the performance of nonlinear multilevel latent variable modeling compared to traditional hierarchical linear modeling. Results suggest that nonlinear multilevel latent variable modeling can more properly estimate and detect contextual effects than the traditional approach. As an empirical illustration, data from the Programme for International Student Assessment were analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:39:y:2014:i:6:p:550-582
    DOI: 10.3102/1076998614559972
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998614559972
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998614559972?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. 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.
    2. Asim Ansari & Kamel Jedidi, 2000. "Bayesian factor analysis for multilevel binary observations," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 475-496, December.
    3. 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.
    4. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
    Full references (including those not matched with items on IDEAS)

    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. Sijia Huang & Li Cai, 2024. "Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 311-341, June.
    2. Peida Zhan & Hong Jiao & Dandan Liao & Feiming Li, 2019. "A Longitudinal Higher-Order Diagnostic Classification Model," Journal of Educational and Behavioral Statistics, , vol. 44(3), pages 251-281, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    8. 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.
    9. 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.
    10. Merkle, Edgar C. & Steyvers, Mark & Mellers, Barbara & Tetlock, Philip E., 2017. "A neglected dimension of good forecasting judgment: The questions we choose also matter," International Journal of Forecasting, Elsevier, vol. 33(4), pages 817-832.
    11. 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.
    12. Luo, Nanyu & Ji, Feng & Han, Yuting & He, Jinbo & Zhang, Xiaoya, 2024. "Fitting item response theory models using deep learning computational frameworks," OSF Preprints tjxab, Center for Open Science.
    13. Sun-Joo Cho & Allan S. Cohen, 2010. "A Multilevel Mixture IRT Model With an Application to DIF," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 336-370, June.
    14. Tuck Siong Chung & Roland T. Rust & Michel Wedel, 2009. "My Mobile Music: An Adaptive Personalization System for Digital Audio Players," Marketing Science, INFORMS, vol. 28(1), pages 52-68, 01-02.
    15. Mariagiulia Matteucci & Bernard Veldkamp, 2015. "The approach of power priors for ability estimation in IRT models," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 917-926, May.
    16. 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.
    17. 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.
    18. 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.
    19. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.
    20. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.

    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:39:y:2014:i:6:p:550-582. 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.