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Category-Level Model Selection for the Sequential G-DINA Model

Author

Listed:
  • Wenchao Ma

    (College of Education, The University of Alabama)

  • Jimmy de la Torre

    (Faculty of Education, The University of Hong Kong)

Abstract

Solving a constructed-response item usually requires successfully performing a sequence of tasks. Each task could involve different attributes, and those required attributes may be “condensed†in various ways to produce the responses. The sequential generalized deterministic input noisy “and†gate model is a general cognitive diagnosis model (CDM) for graded response items of this type. Although a host of dichotomous CDMs with different condensation rules can be used to parameterize the success probability of each task, specifying the most appropriate one remains challenging. If the CDM specified for each task is not in accordance with the underlying cognitive processes, the validity of the inference could be questionable. This study aims to evaluate whether several hypothesis tests, namely, the Wald test using various variance–covariance matrices, the likelihood ratio (LR) test, and the LR test using approximated parameters, can be used to select the appropriate CDMs for each task of graded response items. Simulation studies are conducted to examine the Type I error and power of the hypothesis tests under varied conditions. A data set from the Trends in International Mathematics and Science Study 2007 mathematics assessment is analyzed as an illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:44:y:2019:i:1:p:45-77
    DOI: 10.3102/1076998618792484
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    References listed on IDEAS

    as
    1. Michel Philipp & Carolin Strobl & Jimmy de la Torre & Achim Zeileis, 2018. "On the Estimation of Standard Errors in Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 88-115, February.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. 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.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    6. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    7. M. Jamshidian & R. I. Jennrich, 2000. "Standard errors for EM estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 257-270.
    8. 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.
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