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

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  • 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

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  • 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
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    References listed on IDEAS

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    Cited by:

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    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. 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.

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