Diagnostic classification models for actionable feedback in education: Effects of sample size and assessment length

E-learning is increasingly used to support student learning in higher education. This results in huge amounts of item response data containing valuable information about students' strengths and weaknesses that can be used to provide effective feedback to both students and teachers. However, in current practice, feedback in e-learning is often given in the form of a simple proportion of correctly solved items rather than diagnostic, actionable feedback. Diagnostic classification models (DCMs) provide opportunities to model the item response data from formative assessments in online learning environments and to obtain diagnostic information to improve teaching and learning. This simulation study explores the demands on the data structure (i.e., assessment length, respondent sample size) to apply log-linear DCMs to empirical data. Thereby we provide guidance to educational practitioners on how many items need to be administered to how many students in order to accurately assess skills at different levels of specificity using DCMs. In addition, effects of misspecification of the dimensionality of the assessed skills on model fit indices are explored. Results show that detecting these misspecifications statistically with DCMs can be problematic. Recommendations and implications for educational practice are discussed.