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On the Estimation of Standard Errors in Cognitive Diagnosis Models

Michel Philipp (), Carolin Strobl (), Jimmy de la Torre () and Achim Zeileis ()

Working Papers from Faculty of Economics and Statistics, University of Innsbruck

Abstract: 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 items 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.

Keywords: cognitive diagnosis model; G-DINA; standard errors; information matrix (search for similar items in EconPapers)
JEL-codes: C30 C52 C87 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2016-09
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