The term circumplex was introduced by Guttman (1954) to describe specific patterns in correlation matrices in which, as one moves diagonally away from the main diagonal, intercorrelations at first decrease, then increase. A visual-form hypothesis concerning the magnitude and direction of associations among the variables postulates that, as association strength decreases, the distance between variables on the circumference of a circle increases. Thereby, a circumplex representation implies that both the strength and direction of associations among variables should depend on the distances between the variables on the circumference of a circle.Fabrigar, Visser, and Browne (1997) conducted a review of empirical investigations of circumplex data representations in personality and social psychology. They found two dominant methods of analysis: One was based on exploratory principal components/factor analyses, the other on multidimensional scaling. Because circumplex theories are essentially pictorial representations of the relationships among variables, both of these approaches offer the advantage of yielding graphical representations of the variables' circular ordering. However, neither of these approaches directly examines the extent to which the observed data conform to a circumplex structure. In fact, the two methods can only assess the goodness of fit of two-(or multi-) dimensional scaling/common factor solutions.To overcome this limit, Browne (1992) proposed a covariance structure modeling (CSM) approach for directly testing circumplex structure. (Unless noted otherwise, all discussion of Browne herein relates to Browne, 1992). This approach allows a researcher to examine the extent to which the underlying structure of a sample correlation matrix conforms to a circumplex pattern and to obtain estimates of the locations of the variables on a circle. Browne's CSM approach is based on earlier work by Anderson (1960). Unlike Anderson's approach, however, Browne's can be applied to data in which all variables are positively correlated, as well as to data in which some variables have negative correlations. Thus, Browne's model-unlike Anderson's-may be seen as particularly applicable to personality psychology, where certain personality traits or emotions are expected to be negatively related to each other.A practical advantage of approaches utilizing principal components/factor analysis and multidimensional scaling is their availability in most major statistical programs. In this connection, Browne's CSM approach can be tested using CIRCUM, a DOS program that includes special subroutines specifically designed for analyzing circumplex data, which are appended to a general algorithm for fitting nonstandard models called AUFIT (Browne & Du Toit, 1992). The CIRCUM program allows unconstrained as well as equally spaced estimations of variables' spatial positions around 360º. Constraints can also be applied to the amount of unique 1 variance relative to each variable and to the minimum common score correlation (MCSC) at 180º...