IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v79y2014i3p403-425.html
   My bibliography  Save this article

Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions

Author

Listed:
  • Laine Bradshaw
  • Jonathan Templin

Abstract

Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student’s overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for students, teachers, and other stakeholders. Diagnostic classification models (DCMs) provide multidimensional feedback by using categorical latent variables that represent distinct skills underlying a test that students may or may not have mastered. The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of a unidimensional IRT model and a DCM where the categorical latent variables represent misconceptions instead of skills. In addition to an estimate of ability along a latent continuum, the SICM model provides multidimensional, diagnostic feedback in the form of statistical estimates of probabilities that students have certain misconceptions. Through an empirical data analysis, we show how this additional feedback can be used by stakeholders to tailor instruction for students’ needs. We also provide results from a simulation study that demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions. Copyright The Psychometric Society 2014

Suggested Citation

  • Laine Bradshaw & Jonathan Templin, 2014. "Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 403-425, July.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:3:p:403-425
    DOI: 10.1007/s11336-013-9350-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9350-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9350-4?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. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    2. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    3. Jonathan Templin & Laine Bradshaw, 2013. "Measuring the Reliability of Diagnostic Classification Model Examinee Estimates," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 251-275, July.
    4. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    7. David Thissen & Lynne Steinberg, 1984. "A response model for multiple choice items," Psychometrika, Springer;The Psychometric Society, vol. 49(4), pages 501-519, December.
    8. Jimmy de la Torre & Jeffrey Douglas, 2008. "Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 595-624, December.
    9. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
    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. Michelle M. LaMar, 2018. "Markov Decision Process Measurement Model," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 67-88, March.
    2. Cheng-Hsuan Li & Yi-Jin Ju & Pei-Jyun Hsieh, 2022. "A Nonparametric Weighted Cognitive Diagnosis Model and Its Application on Remedial Instruction in a Small-Class Situation," Sustainability, MDPI, vol. 14(10), pages 1-17, May.
    3. Mark L. Davison & David J. Weiss & Joseph N. DeWeese & Ozge Ersan & Gina Biancarosa & Patrick C. Kennedy, 2023. "A Diagnostic Tree Model for Adaptive Assessment of Complex Cognitive Processes Using Multidimensional Response Options," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 914-941, December.
    4. Lei Guo & Wenjie Zhou & Xiao Li, 2024. "Cognitive Diagnosis Testlet Model for Multiple-Choice Items," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 32-60, February.
    5. Peida Zhan & Hong Jiao & Kaiwen Man & Lijun Wang, 2019. "Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 473-503, August.

    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. Peida Zhan & Wen-Chung Wang & Xiaomin Li, 2020. "A Partial Mastery, Higher-Order Latent Structural Model for Polytomous Attributes in Cognitive Diagnostic Assessments," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 328-351, July.
    2. Jonathan Templin & Laine Bradshaw, 2014. "Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 317-339, April.
    3. Matthew S. Johnson & Sandip Sinharay, 2020. "The Reliability of the Posterior Probability of Skill Attainment in Diagnostic Classification Models," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 5-31, February.
    4. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 973-995, December.
    5. Muhamad Firdaus Mohd Noh & Mohd Effendi Ewan bin Mohd Matore, 2024. "Conundrum and Considerations in Cognitive Diagnostic Assessment for Language Proficiency Evaluation," Information Management and Business Review, AMH International, vol. 16(2), pages 63-72.
    6. Jürgen Heller & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2015. "On the Link between Cognitive Diagnostic Models and Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 995-1019, December.
    7. Xiangyi Liao & Daniel M. Bolt, 2021. "Item Characteristic Curve Asymmetry: A Better Way to Accommodate Slips and Guesses Than a Four-Parameter Model?," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 753-775, December.
    8. Yinghan Chen & Ying Liu & Steven Andrew Culpepper & Yuguo Chen, 2021. "Inferring the Number of Attributes for the Exploratory DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 30-64, March.
    9. Peida Zhan & Hong Jiao & Kaiwen Man & Lijun Wang, 2019. "Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 473-503, August.
    10. Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen, 2023. "Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 613-635, June.
    11. Yinghan Chen & Shiyu Wang, 2023. "Bayesian Estimation of Attribute Hierarchy for Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 810-841, December.
    12. Vassilis Vasdekis & Silvia Cagnone & Irini Moustaki, 2012. "A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 425-441, July.
    13. Hans-Friedrich Köhn & Chia-Yi Chiu, 2017. "A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 112-132, March.
    14. Chun Wang & Steven W. Nydick, 2020. "On Longitudinal Item Response Theory Models: A Didactic," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 339-368, June.
    15. 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.
    16. James Joseph Balamuta & Steven Andrew Culpepper, 2022. "Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA–GAMMA Data Augmentation," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 903-945, September.
    17. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference for the DINA Model," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 569-597, October.
    18. Qingrong Tan & Yan Cai & Fen Luo & Dongbo Tu, 2023. "Development of a High-Accuracy and Effective Online Calibration Method in CD-CAT Based on Gini Index," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 103-141, February.
    19. 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.
    20. Ulf Böckenholt, 2012. "The Cognitive-Miser Response Model: Testing for Intuitive and Deliberate Reasoning," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 388-399, 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:79:y:2014:i:3:p:403-425. 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.