Circumplex Analysis: Addressing Methodological Challenges of Data With Circular Structure

Many psychological traits, such as interpersonal behavior, values, and affect, can be described by a circular structure (e. g. , Gurtman, 1993; Russell et al. , 1989; Schwartz et al. , 2012; Wiggins, 1979). Circumplex models assume specific geometric arrangements of variables, reflected in correlational patterns or factor loadings on two orthogonal axes (L. Guttman, 1954; Tracey, 1997). Factor analysis and principal component analysis (PCA) are widely used to examine such structures. For example, the interpersonal circumplex is defined by the two factors Dominance and Love and underlies popular measures such as the Interpersonal Adjective Scales (IAS; Jacobs Horowitz et al. , 2017). Many models are based on evenly spaced subscales around the circle, and some additionally incorporate an overarching general factor (e. g. , overall interpersonal distress in the IIP). A key challenge in developing circumplex instruments is assigning items to subscales, as adjacent subscales are closely related both conceptually and geometrically. Existing approaches often rely on subjective visual inspection and do not guarantee optimal circumplex spacing. To address methodological challenges in circumplex research, this thesis examined factor analytic approaches as widely used methods for circumplex analysis and developed a new clustering method tailored to circular data. Study 1 investigated local optima in factor rotation procedures, a well-known issue for various rotation methods (Weide https: //github. com/ancleo/ClusterCircSPSS). Despite these contributions, limitations of the thesis research include the use of nonclinical convenience samples and relatively short measures for external variables. Future research should examine additional circular constructs, more complex violations of circumplex assumptions, and combinations of factor rotation procedures with ClusterCirc to further improve circumplex modeling.