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 M2 and the associated root mean square error of approximation (RMSEA2) in item factor analysis were extended to evaluate the fit of CDMs. The findings suggested that the M2 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 RMSEA2 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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