ClusterCirc: Finding item clusters for circumplex instruments

We introduce ClusterCirc, a new method that finds item clusters for circumplex instruments as an alternative to conventional cluster analysis. When developing circumplex instruments, sorting items into subscales can be difficult because of the intended conceptual overlap of subscales in the circular model. ClusterCirc 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 ClusterCirc outperformed conventional cluster analysis in revealing circumplex clusters, especially for large within-cluster distances between items. Sorting accuracy was greater, and effects of data complexity and sample size were more stable in ClusterCirc than in conventional cluster analysis. We also found strong support for ClusterCirc in empirical circumplex data. ClusterCirc 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 ClusterCirc. We provide an R package for ClusterCirc (https://github.com/ancleo/ClusterCirc) with two main functions: ClusterCirc-Data (cc_data) performs ClusterCirc on empirical data. ClusterCirc-Simu (cc_simu) performs a tailored simulation study with the specifications of the data under the assumption of perfect circumplex spacing to assess circumplex fit of the data. We also provide the corresponding SPSS codes for ClusterCirc (https://github.com/ancleo/ClusterCirc_SPSS).