IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v49y2024i5p730-752.html
   My bibliography  Save this article

A Two-Level Adaptive Test Battery

Author

Listed:
  • Wim J. van der Linden

    (University of Twente)

  • Luping Niu
  • Seung W. Choi

    (The University of Texas at Austin)

Abstract

A test battery with two different levels of adaptation is presented: a within-subtest level for the selection of the items in the subtests and a between-subtest level to move from one subtest to the next. The battery runs on a two-level model consisting of a regular response model for each of the subtests extended with a second level for the joint distribution of their abilities. The presentation of the model is followed by an optimized MCMC algorithm to update the posterior distribution of each of its ability parameters, select the items to Bayesian optimality, and adaptively move from one subtest to the next. Thanks to extremely rapid convergence of the Markov chain and simple posterior calculations, the algorithm can be used in real-world applications without any noticeable latency. Finally, an empirical study with a battery of short diagnostic subtests is shown to yield score accuracies close to traditional one-level adaptive testing with subtests of double lengths.

Suggested Citation

  • Wim J. van der Linden & Luping Niu & Seung W. Choi, 2024. "A Two-Level Adaptive Test Battery," Journal of Educational and Behavioral Statistics, , vol. 49(5), pages 730-752, October.
    • Handle: RePEc:sae:jedbes:v:49:y:2024:i:5:p:730-752
    DOI: 10.3102/10769986231209447
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/10769986231209447
    Download Restriction: no
    File URL: https://libkey.io/10.3102/10769986231209447?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. Wim J. van der Linden & Hao Ren, 2020. "A Fast and Simple Algorithm for Bayesian Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 58-85, February.
    2. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    3. Hao Ren & Wim J. van der Linden & Qi Diao, 2017. "Continuous Online Item Calibration: Parameter Recovery and Item Utilization," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 498-522, June.
    4. Wim J. van der Linden & Bingnan Jiang, 2020. "A Shadow-Test Approach to Adaptive Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 301-321, 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. Wim J. van der Linden & Bingnan Jiang, 2020. "A Shadow-Test Approach to Adaptive Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 301-321, June.
    2. Napoleón Vargas Jurado & Kent M. Eskridge & Stephen D. Kachman & Ronald M. Lewis, 2018. "Using a Bayesian Hierarchical Linear Mixing Model to Estimate Botanical Mixtures," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 190-207, June.
    3. Etienne Côme & Nicolas Jouvin & Pierre Latouche & Charles Bouveyron, 2021. "Hierarchical clustering with discrete latent variable models and the integrated classification likelihood," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 957-986, December.
    4. Aaron T L Lun & Hervé Pagès & Mike L Smith, 2018. "beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types," PLOS Computational Biology, Public Library of Science, vol. 14(5), pages 1-15, May.
    5. Tilman M. Davies & Sudipto Banerjee & Adam P. Martin & Rose E. Turnbull, 2022. "A nearest‐neighbour Gaussian process spatial factor model for censored, multi‐depth geochemical data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 1014-1043, August.
    6. Helmut Lutkepohl & Fei Shang & Luis Uzeda & Tomasz Wo'zniak, 2024. "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference," Papers 2404.11057, arXiv.org.
    7. 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).
    8. Cardona Jiménez, Johnatan & de B. Pereira, Carlos A., 2021. "Assessing dynamic effects on a Bayesian matrix-variate dynamic linear model: An application to task-based fMRI data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    9. Lu Chen & Balgobin Nandram, 2023. "Bayesian Logistic Regression Model for Sub-Areas," Stats, MDPI, vol. 6(1), pages 1-23, January.
    10. Jos'e Vin'icius de Miranda Cardoso & Jiaxi Ying & Daniel Perez Palomar, 2020. "Algorithms for Learning Graphs in Financial Markets," Papers 2012.15410, arXiv.org.
    11. Batarce, Marco, 2024. "Estimation of discrete choice models with error in variables: An application to revealed preference data with aggregate service level variables," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
    12. Maximilian Böck & Martin Feldkircher & Florian Huber, 2020. "BGVAR: Bayesian Global Vector Autoregressions with Shrinkage Priors in R," Globalization Institute Working Papers 395, Federal Reserve Bank of Dallas.
    13. Shen, Yunyi & Olson, Erik R. & Van Deelen, Timothy R., 2021. "Spatially explicit modeling of community occupancy using Markov Random Field models with imperfect observation: Mesocarnivores in Apostle Islands National Lakeshore," Ecological Modelling, Elsevier, vol. 459(C).
    14. Zhe Yu & Raquel Prado & Erin Burke Quinlan & Steven C. Cramer & Hernando Ombao, 2016. "Understanding the Impact of Stroke on Brain Motor Function: A Hierarchical Bayesian Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 549-563, April.
    15. Matthew Pietrosanu & Jueyu Gao & Linglong Kong & Bei Jiang & Di Niu, 2021. "Advanced algorithms for penalized quantile and composite quantile regression," Computational Statistics, Springer, vol. 36(1), pages 333-346, March.
    16. Jonathan Berrisch & Florian Ziel, 2021. "CRPS Learning," Papers 2102.00968, arXiv.org, revised Nov 2021.
    17. Ankargren, Sebastian & Jonéus, Paulina, 2021. "Simulation smoothing for nowcasting with large mixed-frequency VARs," Econometrics and Statistics, Elsevier, vol. 19(C), pages 97-113.
    18. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    19. François Bachoc & Marc G Genton & Klaus Nordhausen & Anne Ruiz-Gazen & Joni Virta, 2020. "Spatial blind source separation," Biometrika, Biometrika Trust, vol. 107(3), pages 627-646.
    20. Moores, Matthew T. & Hargrave, Catriona E. & Deegan, Timothy & Poulsen, Michael & Harden, Fiona & Mengersen, Kerrie, 2015. "An external field prior for the hidden Potts model with application to cone-beam computed tomography," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 27-41.

    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:49:y:2024:i:5:p:730-752. 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.