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On the Estimation of Standard Errors in Cognitive Diagnosis Models


Philipp, Michel; Strobl, Carolin; de la Torre, Jimmy; Zeileis, Achim (2018). On the Estimation of Standard Errors in Cognitive Diagnosis Models. Journal of Educational and Behavioral Statistics, 43(1):88-115.

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 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.

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 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:06 Faculty of Arts > Institute of Psychology
Dewey Decimal Classification:150 Psychology
Uncontrolled Keywords:DoktoratPsych Erstautor
Date:2018
Deposited On:30 Jan 2018 15:42
Last Modified:30 Jul 2018 06:54
Publisher:Sage Publications Ltd.
ISSN:1076-9986
OA Status:Closed
Publisher DOI:https://doi.org/10.3102/1076998617719728

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