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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.
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Liu et al. (2015) studied this question.
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