IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i1d10.1007_s11336-022-09872-8.html
   My bibliography  Save this article

On Reverse Shrinkage Effects and Shrinkage Overshoot

Author

Listed:
  • Pascal Jordan

    (University of Hamburg)

Abstract

Given a squared Euclidean norm penalty, we examine some less well-known properties of shrinkage estimates. In particular, we highlight that it is possible for some components of the shrinkage estimator to be placed further away from the prior mean than the original estimate. An analysis of this effect is provided within three different modeling settings—encompassing linear, logistic, and ordinal regression models. Additional simulations show that the outlined effect is not a mathematical artefact, but likely to occur in practice. As a byproduct, they also highlight the possibilities of sign reversals (“overshoots”) for shrinkage estimates. We point out practical consequences and challenges, which might arise from the observed effects with special emphasis on psychometrics.

Suggested Citation

  • Pascal Jordan, 2023. "On Reverse Shrinkage Effects and Shrinkage Overshoot," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 274-301, March.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:1:d:10.1007_s11336-022-09872-8
    DOI: 10.1007/s11336-022-09872-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-022-09872-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-022-09872-8?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 287-308, September.
    2. Shelby Haberman & Sandip Sinharay, 2010. "Reporting of Subscores Using Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 209-227, June.
    3. Pascal Jordan & Martin Spiess, 2012. "Generalizations of Paradoxical Results in Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 127-152, January.
    4. Daniel Segall, 1996. "Multidimensional adaptive testing," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 331-354, June.
    5. Wim Linden, 2012. "On Compensation in Multidimensional Response Modeling," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 21-30, January.
    6. Pascal Jordan & Martin Spiess, 2018. "A New Explanation and Proof of the Paradoxical Scoring Results in Multidimensional Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 831-846, December.
    7. Giles Hooker, 2010. "On Separable Tests, Correlated Priors, and Paradoxical Results in Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 694-707, December.
    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. Pascal Jordan & Martin Spiess, 2018. "A New Explanation and Proof of the Paradoxical Scoring Results in Multidimensional Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 831-846, December.
    2. Pascal Jordan & Martin Spiess, 2018. "On Fair Person Classification Based on Efficient Factor Score Estimates in the Multidimensional Factor Analysis Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 563-585, September.
    3. Lihua Yao, 2012. "Multidimensional CAT Item Selection Methods for Domain Scores and Composite Scores: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 495-523, July.
    4. Matthew D. Finkelman & Giles Hooker & Zhen Wang, 2010. "Prevalence and Magnitude of Paradoxical Results in Multidimensional Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 744-761, December.
    5. 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.
    6. Chun Wang, 2014. "Improving Measurement Precision of Hierarchical Latent Traits Using Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 452-477, December.
    7. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    8. Steven Andrew Culpepper & James Joseph Balamuta, 2017. "A Hierarchical Model for Accuracy and Choice on Standardized Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 820-845, September.
    9. Chun Wang & David J. Weiss & Zhuoran Shang, 2019. "Variable-Length Stopping Rules for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 749-771, September.
    10. Edison M. Choe & Jinming Zhang & Hua-Hua Chang, 2018. "Sequential Detection of Compromised Items Using Response Times in Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 650-673, September.
    11. Ping Chen & Chun Wang, 2016. "A New Online Calibration Method for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 674-701, September.
    12. Sora Lee & Daniel M. Bolt, 2018. "Asymmetric Item Characteristic Curves and Item Complexity: Insights from Simulation and Real Data Analyses," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 453-475, June.
    13. Daniel Segall, 2001. "General ability measurement: An application of multidimensional item response theory," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 79-97, March.
    14. Yi-Hsuan Lee & Zhiliang Ying, 2015. "A Mixture Cure-Rate Model for Responses and Response Times in Time-Limit Tests," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 748-775, September.
    15. Maria Bolsinova & Paul Boeck & Jesper Tijmstra, 2017. "Modelling Conditional Dependence Between Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1126-1148, December.
    16. Frederik Coomans & Abe Hofman & Matthieu Brinkhuis & Han L J van der Maas & Gunter Maris, 2016. "Distinguishing Fast and Slow Processes in Accuracy - Response Time Data," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-19, May.
    17. Matthias Davier & Shelby Haberman, 2014. "Hierarchical Diagnostic Classification Models Morphing into Unidimensional ‘Diagnostic’ Classification Models—A Commentary," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 340-346, April.
    18. Sandip Sinharay, 2015. "The Asymptotic Distribution of Ability Estimates," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 511-528, October.
    19. Susu Zhang & Zhi Wang & Jitong Qi & Jingchen Liu & Zhiliang Ying, 2023. "Accurate Assessment via Process Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 76-97, March.
    20. Ping Chen, 2017. "A Comparative Study of Online Item Calibration Methods in Multidimensional Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 42(5), pages 559-590, October.

    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:spr:psycho:v:88:y:2023:i:1:d:10.1007_s11336-022-09872-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.