K-means clustering of item characteristic curves and item information curves via functional principal component analysis

The assessment of students’ performances and learning skills plays a key role in the educational context. Common tools for analyzing test data are item response theory (IRT) models. They bring interesting outputs such as item characteristic curves (ICCs) and item information curves (IICs), which provide the probability of correctly answering items and the amount of information for different ability levels, respectively. In recent decades, many studies have pointed out the importance of clustering methods in the IRT context. Nevertheless, tests assessment through IRT models and the related clustering algorithms generally focus on the analysis of item parameters. These approaches are certainly more simple but parameters are synthetic indicators of a function’s behavior, and thus some interesting information within the domain may be lost. Because ICCs and IICs are functions in a continuous domain (the subject ability), this research proposes to treat them with the functional data analysis (FDA) approach. Specifically, this study focuses on the use of the K-means clustering method for analysing ICCs and IICs via the functional principal component analysis. We show that the combined use of FDA and cluster analysis reveals interesting insights in the IRT context. The final aim of this approach is to provide practitioners and scholars with additional tools for the assessment of tests for students’ evaluation.