ClusterCirc: Finding item clusters for circumplex instruments

Abstract

We introduce Cluster-Circ, a new method that finds item clusters as possible subscales for circumplex instruments. When developing circumplex instruments, sorting items into subscales can be difficult because of the intended conceptual overlap of subscales in the circular model. Cluster-Circ provides a statistical solution for sorting items into subscales by finding item clusters with optimal circumplex spacing of both items and clusters. In a simulation study, we found that Cluster-Circ outperformed conventional cluster analysis in revealing circumplex clusters, especially when within-cluster distances between items increased. Sorting accuracy was greater and effects of data complexity and sample size were more stable in Cluster-Circ than in conventional cluster analysis. We also found strong support for Cluster-Circ in empirical circumplex data. Cluster-Circ sorting resulted in subscales with good scale properties and greater circumplex fit than the original subscales and subscales based on cluster analysis. We recommend a sample size between n = 500 and 1,000 to ensure high sorting accuracy of Cluster-Circ. We provide SPSS codes for Cluster-Circ and for a tailored simulation study with perfect circumplexity and the specifications of the respective dataset for better interpretation of Cluster-Circ results (Supplement).