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A Cognitive Diagnosis Model for Continuous Response

Author

Listed:
  • Nathan D. Minchen

    (Rutgers, The State University of New Jersey)

  • Jimmy de la Torre

    (The University of Hong Kong)

  • Ying Liu

    (University of Southern California)

Abstract

Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to extract information with diagnostic value from continuous response data, a multidimensional skills diagnosis model for continuous response is proposed. An expectation-maximization implementation of marginal maximum likelihood estimation is developed to estimate its parameters. The viability of the proposed model is shown via a simulation study and a real data example. The proposed model is also shown to provide a substantial improvement in attribute classification when compared to a model based on dichotomized continuous responses.

Suggested Citation

  • Nathan D. Minchen & Jimmy de la Torre & Ying Liu, 2017. "A Cognitive Diagnosis Model for Continuous Response," Journal of Educational and Behavioral Statistics, , vol. 42(6), pages 651-677, December.
    • Handle: RePEc:sae:jedbes:v:42:y:2017:i:6:p:651-677
    DOI: 10.3102/1076998617703060
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    References listed on IDEAS

    as
    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Fumiko Samejima, 1973. "Homogeneous case of the continuous response model," Psychometrika, Springer;The Psychometric Society, vol. 38(2), pages 203-219, June.
    3. Ying Cheng, 2009. "When Cognitive Diagnosis Meets Computerized Adaptive Testing: CD-CAT," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 619-632, December.
    4. Fumiko Samejima, 1974. "Normal ogive model on the continuous response level in the multidimensional latent space," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 111-121, March.
    5. Yvonnick Noel, 2014. "A Beta Unfolding Model for Continuous Bounded Responses," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 647-674, October.
    6. Gunter Maris & Han Maas, 2012. "Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 615-633, October.
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