Incremental Validity of Multidimensional Proficiency Scores from Diagnostic Classification Models: An Illustration for Elementary School Mathematics

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.