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Joint Maximum Likelihood Estimation for Diagnostic Classification Models

Author

Listed:
  • Chia-Yi Chiu

    (Rutgers, The State University of New Jersey)

  • Hans-Friedrich Köhn

    (University of Illinois at Urbana-Champaign)

  • Yi Zheng

    (Arizona State University)

  • Robert Henson

    (University of North Carolina)

Abstract

Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test.

Suggested Citation

  • Chia-Yi Chiu & Hans-Friedrich Köhn & Yi Zheng & Robert Henson, 2016. "Joint Maximum Likelihood Estimation for Diagnostic Classification Models," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1069-1092, December.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9534-9
    DOI: 10.1007/s11336-016-9534-9
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    References listed on IDEAS

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    1. 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.
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    3. Chia-Yi Chiu & Jeffrey Douglas & Xiaodong Li, 2009. "Cluster Analysis for Cognitive Diagnosis: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 633-665, December.
    4. Kikumi K. Tatsuoka, 1985. "A Probabilistic Model for Diagnosing Misconceptions By The Pattern Classification Approach," Journal of Educational and Behavioral Statistics, , vol. 10(1), pages 55-73, March.
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    Cited by:

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    4. Zhang, Haoran & Chen, Yunxiao & Li, Xiaoou, 2020. "A note on exploratory item factor analysis by singular value decomposition," LSE Research Online Documents on Economics 104166, London School of Economics and Political Science, LSE Library.

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