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Abstract
Diagnostic classification models (DCMs) hold great potential for applications in summative and formative assessment by providing discrete multivariate proficiency scores that yield statistically driven classifications of students. Using data from a newly developed diagnostic arithmetic assessment that was administered to 2032 fourth-grade students in Germany, we evaluated whether the multidimensional proficiency scores from the best-fitting DCM have an added value, over and above the unidimensional proficiency score from a simpler unidimensional item response theory model, in explaining variance in external (a) school grades in mathematics and (b) unidimensional proficiency scores from a standards-based large-scale assessment of mathematics. Results revealed high classification reliabilities as well as interpretable parameter estimates for items and students for the best-fitting DCM. However, while DCM scores were moderately correlated with both external criteria, only a negligible incremental validity of the multivariate attribute scores was found.
FUNDING
This research project was, in part, supported by grant RU 1424/3-1 from the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) in the Priority Program 1293 “Models of Competencies for the Assessment of Individual Learning Outcomes and the Evaluation of Educational Processes” and, in part, by a General Research Board (GRB) award, which was awarded to the second author for the summer 2009. The opinions, findings, and conclusions or recommendations in this paper are those of the authors and do not necessarily reflect the views of the funding agencies, cooperating institutions, or other individuals.