Journal
JOURNAL OF EDUCATIONAL AND BEHAVIORAL STATISTICS
Volume 43, Issue 1, Pages 88-115Publisher
SAGE PUBLICATIONS INC
DOI: 10.3102/1076998617719728
Keywords
cognitive diagnosis model; G-DINA; standard errors; information matrix
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Cognitive diagnosis models (CDMs) are an increasingly popular method to assess mastery or nonmastery of a set of fine-grained abilities in educational or psychological assessments. Several inference techniques are available to quantify the uncertainty of model parameter estimates, to compare different versions of CDMs, or to check model assumptions. However, they require a precise estimation of the standard errors (or the entire covariance matrix) of the model parameter estimates. In this article, it is shown analytically that the currently widely used form of calculation leads to underestimated standard errors because it only includes the item parameters but omits the parameters for the ability distribution. In a simulation study, we demonstrate that including those parameters in the computation of the covariance matrix consistently improves the quality of the standard errors. The practical importance of this finding is discussed and illustrated using a real data example.
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