IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v83y2018i3d10.1007_s11336-018-9610-4.html
   My bibliography  Save this article

Robust Measurement via A Fused Latent and Graphical Item Response Theory Model

Author

Listed:
  • Yunxiao Chen

    (Emory University)

  • Xiaoou Li

    (University of Minnesota)

  • Jingchen Liu

    (Columbia University)

  • Zhiliang Ying

    (Columbia University)

Abstract

Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits.

Suggested Citation

  • Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:3:d:10.1007_s11336-018-9610-4
    DOI: 10.1007/s11336-018-9610-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-018-9610-4
    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/s11336-018-9610-4?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. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Edward Ip, 2002. "Locally dependent latent trait model and the dutch identity revisited," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 367-386, September.
    3. Edward Ip & Yuchung Wang & Paul Boeck & Michel Meulders, 2004. "Locally dependent latent trait model for polytomous responses with application to inventory of hostility," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 191-216, June.
    4. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    5. Jianan Sun & Yunxiao Chen & Jingchen Liu & Zhiliang Ying & Tao Xin, 2016. "Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$ L 1 Regularization," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 921-939, December.
    6. Jingchen Liu, 2017. "On the Consistency of Q-Matrix Estimation: A Commentary," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 523-527, June.
    7. Johan Braeken, 2011. "A Boundary Mixture Approach to Violations of Conditional Independence," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 57-76, January.
    8. Carolyn Anderson & Hsiu-Ting Yu, 2007. "Log-Multiplicative Association Models as Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 5-23, March.
    9. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    10. Paul Holland, 1990. "The Dutch Identity: A new tool for the study of item response models," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 5-18, March.
    11. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    12. Yunxiao Chen & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2015. "Statistical Analysis of Q -Matrix Based Diagnostic Classification Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 850-866, June.
    13. Wen-Hung Chen & David Thissen, 1997. "Local Dependence Indexes for Item Pairs Using Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 22(3), pages 265-289, September.
    14. Sacha Epskamp & Mijke Rhemtulla & Denny Borsboom, 2017. "Generalized Network Psychometrics: Combining Network and Latent Variable Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 904-927, December.
    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. 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.
    3. Nussbaum, Frank & Giesen, Joachim, 2020. "Pairwise sparse + low-rank models for variables of mixed type," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    4. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    5. Jinsong Chen, 2020. "A Partially Confirmatory Approach to the Multidimensional Item Response Theory with the Bayesian Lasso," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 738-774, September.

    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. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    2. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2013. "Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model," Journal of Educational and Behavioral Statistics, , vol. 38(1), pages 32-60, February.
    3. Minjeong Jeon & Sophia Rabe-Hesketh, 2016. "An autoregressive growth model for longitudinal item analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 830-850, September.
    4. Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    5. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    6. Nana Kim & Daniel M. Bolt & James Wollack, 2022. "Noncompensatory MIRT For Passage-Based Tests," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 992-1009, September.
    7. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    8. Chenchen Ma & Jing Ouyang & Gongjun Xu, 2023. "Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 175-207, March.
    9. 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.
    10. Michela Gnaldi & Silvia Bacci & Thiemo Kunze & Samuel Greiff, 2020. "Students’ Complex Problem Solving Profiles," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 469-501, June.
    11. 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.
    12. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    13. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    14. Youn Seon Lim & Fritz Drasgow, 2019. "Conditional Independence and Dimensionality of Cognitive Diagnostic Models: a Test for Model Fit," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 295-305, July.
    15. Hudson Golino & Alexander P. Christensen & Robert Moulder & Seohyun Kim & Steven M. Boker, 2022. "Modeling Latent Topics in Social Media using Dynamic Exploratory Graph Analysis: The Case of the Right-wing and Left-wing Trolls in the 2016 US Elections," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 156-187, March.
    16. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    17. Yuri Goegebeur & Paul Boeck & James Wollack & Allan Cohen, 2008. "A Speeded Item Response Model with Gradual Process Change," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 65-87, March.
    18. Joachim Büschken & Thomas Otter & Greg M. Allenby, 2013. "The Dimensionality of Customer Satisfaction Survey Responses and Implications for Driver Analysis," Marketing Science, INFORMS, vol. 32(4), pages 533-553, July.
    19. Gülden Kaya Uyanik & Levent Ertuna, 2022. "Examination of Testlet Effect in Open-Ended Items," SAGE Open, , vol. 12(1), pages 21582440221, February.
    20. Svend Kreiner & Karl Christensen, 2011. "Item Screening in Graphical Loglinear Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 228-256, April.

    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:83:y:2018:i:3:d:10.1007_s11336-018-9610-4. 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.