Circular Modelling of Circumplex Measurements for Interpersonal Behavior

This article describes a new way to analyze data from the interpersonal circumplex (IPC) for interpersonal behavior. Instead of analyzing Agency and Communion separately or analyzing the IPC's octants, we propose using a circular regression model that allows us to investigate effects on a blend of Agency and Communion. The proposed circular model is called a projected normal (PN) model. We illustrate the use of a PN mixed-effects model on three repeated measures data sets with circumplex measurements from interpersonal and educational psychology. This model allows us to detect different types of patterns in the data and provides a more valid analysis of circumplex data. In addition to being able to investigate the effect on the location (mean) of scores on the IPC, we can also investigate effects on the spread (variance) of scores on the IPC. We also introduce new tools that help interpret the fixed and random effects of PN models.