Pre-print: Detecting Sinusoidal Patterns from Circumplex Models of Psychological Constructs

An interesting feature of circumplex models of psychological constructs is that they may yield a sinusoidal (i.e., sine wave) pattern of relations between the elements in the model and variables that are external to the model. Thus far, however, the fit to a sinusoidal pattern has been evaluated with visual inspection or arbitrary means of parsing patterns of association. In this research, we developed and validated a sinusoidal fit index (SFI). We then applied the SFI to Schwartz’s original (1992) and revised (Schwartz et al., 2012) models of human values and the circumplex model of interpersonal problems (Alden et al., 1990). Examination of data from the European Social Survey revealed adequate to very good sinusoidal fit of Schwartz’s model to two-thirds of the variables in the survey. Data from published papers revealed very good fit to all variables in the model of interpersonal problems. The results also suggested potential adjustments to the scoring of human values and to the ordering of the values. Discussion focuses on implications for research on values, applications to other circumplex models of individual difference, and broad implications for detecting sinusoidal patterns in data.