Cluster Analysis of Angular Data in Applications of Multidimensional Item-Response Theory

A procedure for interpreting multiple-discrimination indices obtained from a multidimensional item-response theory (MIRT) analysis is described and demonstrated. The procedure consists of converting discrimination parameter estimates to direction cosines and cluster analyzing the angular distances between item vectors, grouping together items with similar orientations in the theta space. The procedure is suggested as an alternative to conventional item factor analysis for investigating issues related to test dimensionality within a single test form and between alternate forms of a test.