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An Application of M2 Statistic to Evaluate the Fit of Cognitive Diagnostic Models

Author

Listed:
  • Yanlou Liu

    (Beijing Normal University)

  • Wei Tian

    (Beijing Normal University)

  • Tao Xin

    (Beijing Normal University)

Abstract

The fit of cognitive diagnostic models (CDMs) to response data needs to be evaluated, since CDMs might yield misleading results when they do not fit the data well. Limited-information statistic M 2 and the associated root mean square error of approximation (RMSEA 2 ) in item factor analysis were extended to evaluate the fit of CDMs. The findings suggested that the M 2 statistic has proper empirical Type I error rates and good statistical power, and it could be used as a general statistical tool. More importantly, we found that there was a strong linear relationship between mean marginal misclassification rates and RMSEA 2 when there was model–data misfit. The evidence demonstrated that .030 and .045 could be reasonable thresholds for excellent and good fit, respectively, under the saturated log-linear cognitive diagnosis model.

Suggested Citation

  • Yanlou Liu & Wei Tian & Tao Xin, 2016. "An Application of M2 Statistic to Evaluate the Fit of Cognitive Diagnostic Models," Journal of Educational and Behavioral Statistics, , vol. 41(1), pages 3-26, February.
    • Handle: RePEc:sae:jedbes:v:41:y:2016:i:1:p:3-26
    DOI: 10.3102/1076998615621293
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    References listed on IDEAS

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    1. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
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    3. Robert Mislevy, 1986. "Bayes modal estimation in item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 177-195, June.
    Full references (including those not matched with items on IDEAS)

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