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

Yanlou Liu, Wei Tian and Tao Xin
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Yanlou Liu: Beijing Normal University
Wei Tian: Beijing Normal University
Tao Xin: Beijing Normal University

Journal of Educational and Behavioral Statistics, 2016, vol. 41, issue 1, 3-26

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.

Keywords: cognitive diagnosis models; limited-information test statistics; goodness-of-fit; approximate fit (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:41:y:2016:i:1:p:3-26

DOI: 10.3102/1076998615621293

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