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On the Estimation of Standard Errors in Cognitive Diagnosis Models

Author

Listed:
  • Michel Philipp
  • Carolin Strobl
  • Jimmy de la Torre
  • Achim Zeileis

Abstract

Cognitive diagnosis models (CDMs) are an increasingly popular method to assess mastery or nonmastery of a set of fine-grained abilities in educational or psychological assessments. Several inference techniques are available to quantify the uncertainty of model parameter estimates, to compare different versions of CDMs or to check model assumptions. However, they require a precise estimation of the standard errors (or the entire covariance matrix) of the model parameter estimates. In this article, it is shown analytically that the currently widely used form of calculation leads to underestimated standard errors because it only includes the items parameters, but omits the parameters for the ability distribution. In a simulation study, we demonstrate that including those parameters in the computation of the covariance matrix consistently improves the quality of the standard errors. The practical importance of this finding is discussed and illustrated using a real data example.

Suggested Citation

  • Michel Philipp & Carolin Strobl & Jimmy de la Torre & Achim Zeileis, 2016. "On the Estimation of Standard Errors in Cognitive Diagnosis Models," Working Papers 2016-25, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2016-25
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    References listed on IDEAS

    as
    1. Ke-Hai Yuan & Ying Cheng & Jeff Patton, 2014. "Information Matrices and Standard Errors for MLEs of Item Parameters in IRT," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 232-254, April.
    2. 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.
    3. 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.
    4. David Thissen & Howard Wainer, 1982. "Some standard errors in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 397-412, December.
    5. Steven Andrew Culpepper, 2015. "Bayesian Estimation of the DINA Model With Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 454-476, October.
    6. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
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    Cited by:

    1. Wenchao Ma & Jimmy de la Torre, 2019. "Category-Level Model Selection for the Sequential G-DINA Model," Journal of Educational and Behavioral Statistics, , vol. 44(1), pages 45-77, February.
    2. 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.
    3. Kazuhiro Yamaguchi & Jonathan Templin, 2022. "Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1390-1421, December.

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    More about this item

    Keywords

    cognitive diagnosis model; G-DINA; standard errors; information matrix;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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