The Interpersonal Circumplex
The birth of the contemporary movement in interpersonal psychology and its use of the circumplex was marked by a series of articles that appeared in the early 1950s (Freedman, Leary, Ossario, & Coffey, 1951; LaForge, Leary, Naboisek, Coffey, & Freedman, 1954). In an effort to elucidate the processes operating in group psychotherapy sessions, these investigators collected, transcribed and analyzed hundreds of hours of group therapy sessions (Freedman, 1985). By way of developing a system of coding, the structural model now recognized as the Interpersonal Circle was created around the two dimensions of dominance-submission and affiliation-aggression.
Although this group developed their circle without the advantage of Guttman's (1954) model of a circumplex, their decision to order the 16 interpersonal variables in a circular fashion around the axes of control and affiliation was, as Wiggins (1982) put it, "particularly prescient" (p. 187).
There are a number of distinct advantages in using a circumplex as a structural model. Before discussing these advantages and how they may be exploited in personality research, it might be helpful to define circumplex.
In a very general sense, a circumplex is a two-dimensional model that describes expected relationships among a number of variables (Guttman, 1954). The relationship among variables is said to be circular, implying an ordering of variables that is without beginning or end, in which similar variables are closer to one another on the circle, variables that are semantic or behavioral opposites are located directly across the circle (i.e., through the origin) and variables that are unrelated or orthogonal are separated by angles of ninety degrees. In the interpersonal domain, the interpersonal circle (Freedman, et al., 1951; Kiesler, 1983; LaForge, et al., 1954; Leary, 1957; Wiggins, 1979; Wiggins, Phillips & Trapnell, 1989) is generally organized around orthogonal axes of control (or status) and affiliation (or warmth). Characteristics represented on the circle as sampled by various circle measures include interpersonal traits, actions, problems and impacts.
Using Kiesler's (1983) Circle as a model (see Figure 1), it can be seen that interpersonal characteristics located adjacent to one another on the circle (e.g., Sociable and Friendly) are quite similar. Correspondingly, characteristics located on opposite sides of the circle are semantic or behavioral opposites (e.g., Friendly and Hostile) while those at right angles to one another (e.g.,Friendly and Dominant) are conceptually unrelated. It should be noted that, while the circle depicted in Figure 1 is represented by 16 categories or segments (labelled A through P), several other current models (initially, those of Wiggins and colleagues) combine adjacent sixteenths to produce a circle composed of octant categories (often labelled PA, BC, DE, etc.). The decision to represent the circle via 8 or 16 categories is generally one of practicality; the gains in specificity of measuring the circumplex with 16 scales are offset by greater psychometric difficulties.
Figure 1. The 1982 Interpersonal Circle (Kiesler, 1983)
There are some assumptions upon which two-dimensional interpersonal circle models are based. First, behaviors or dispositions that fall between two axes (e.g., sector O, Exhibitionistic, in Figure 1) are construed as blends of those two primary dimensions (Kiesler, 1991). Conceptually, then, a scale located equidistantly between the Friendly and Dominant axes is considered to be a blend of equal parts of Friendliness and Dominance. Scales closer to a given axis (e.g., sector P, Assured, in Figure 1) should reflect more strongly, in their content, attributes of the nearest axis. Referring again to Figure 1, we would expect Competitive (sector B) behaviors or dispositions to have a much stronger dominance component and a much weaker hostility component than Cold behaviors (sector D).
Returning to a more general discussion of circumplexes, there are a number of basic features that must be addressed. First, as mentioned above, one characteristic of the model is that there is a circular ordering of variables. Consulting Figure 2, and using point X as a reference point, there is a predicted pattern of relationship between X and each of the other variables.
Placement of Octant Scales on the Interpersonal Circle and Their Displacement (in Degrees) from Octant LM
That correlational pattern can be represented in the following equation:
In a loose sense, variable X has a circular relationship with variables PA through NO; proceeding counterclockwise, its correlation is highest with PA, decreases with BC, DE, FG until it reaches its lowest value with HI, at which point the pattern reverses and the correlations increase in magnitude through JK, LM and NO.
There are more exacting definitions of circumplexity, however, and exploration of these definitions reveals many of the more powerful properties of this structural model. As hinted at in the preceding example, there is a characteristic relationship among variables in a two-dimensional circumplex. In such a circumplex, measured perfectly and without error by eight scales evenly placed about the circumference, the pattern of correlations shown in Table 1 will be found (see, e.g., Wiggins, Steiger, & Gaelick, 1981).
Correlations Among Octant Scales in a Perfect Two-Dimensional Circumplex
A major advantage of the model is the ability of investigators to use principles of trigonometry in describing and testing its structural features (Gurtman, 1992; Guttman, 1954; Wiggins, 1968). In the perfect, two-dimensional circumplex described above, for example, it can be seen that the correlation between any two scales is actually the cosine of their angle of separation (Comrey, 1973; Gurtman, 1993). Referring again to Figure 2, variables separated by 45 degrees (e.g., PA & BC) correlate .707, those separated by 90 degrees (e.g., PA & DE) are orthogonal, and so on. Table 2 lists the degrees of separation between variables in a perfect two-dimensional circumplex and their associated correlations.
Angular Displacement (in Degrees) Between Scales and Associated Correlations
An extension of these trigonometric features allows one to calculate theoretically derived factor scores for the two orthogonal dimensions, or axes, based on scores of the eight scales (LaForge, 1977). In the example, the vertical axis, corresponding to the control factor (or DOM), is anchored at its poles by PA and HI, and can be calculated as a function of the scores on all eight scales as follows:
The horizontal axis, representing the affiliation factor (or LOV), is defined by DE and LM at its poles, could similarly be calculated from the eight scale scores:
Two more concepts important to a discussion of circumplexes will now be introduced. The first concerns determination of the angular location of a variable or scale with respect to the two factors or dimensions. Angular location on the circumplex is more precisely referred to as angular displacement from 0 degrees. By convention, the friendly pole of the affiliation axis (denoted by scale LM) represents the point of reference (i.e., zero degrees) to which other locations on the circle are compared. Thus, NO is located at 45 degrees, PA at 90, BC at 135, and so on, as illustrated in Figure 2. If the factor scores for DOM and LOV are known, the angular displacement, expressed in radians, can be determined using as follows:
Similarly, another important calculation that can be made once LOV and DOM scores are known is that of vector length. Vector length specifies a variable's distance from the center of a circle and represents the extent to which the variable loads on (or is represented by) the two interpersonal factors (LaForge, 1977; Wiggins et al., 1989; Gurtman, 1993). In a very general sense, variables that show strong interpersonal characteristics will have a large vector length (placing them nearer the circumference of the circle than the center), while those unrelated to LOV and DOM will have a small value for vector length. Using the distance formula of Pythagoras, vector length (VL) is calculated as:
Although a thorough, technical discussion of the advantages of the trigonometric underpinnings of this model is beyond the scope of the current discussion, two advantages are particularly salient for the proposed project. Most importantly, Fisher, Heise, Bohrnstedt, and Lucke (1985) derived computations based upon the circle's trigonometric properties, that allow comparison of an empirical circumplex to a theoretical circumplex. This produces a coefficient, similar to a correlation, that expresses how well a data-based circumplex fits the theoretical model it purports to represent (see Statistics page for a more thorough discussion). A second advantage of the application of trigonometry, already mentioned, is the ability it provides to compute the location of an external variable on the circle if it's correlation with the two main factors or dimensions is known. Gurtman (1992) has masterfully demonstrated how this can be accomplished to evaluate the 'goodness of fit' of a variable or an item onto the circumplex; in other words, this procedure can determine the degree to which any personality measure is empirically related to the interpersonal behavior domain.
This structural model has particular relevance to personality psychology. The interpersonal circle variables may be seen as part of a nomological net (Cronbach & Meehl, 1955; Gurtman, 1992) that can help in the determination of convergent and discriminant validity of extraneous variables. Other personality variables that are theorized as related to, or not related to, interpersonal characteristics may thus be tested to see if they 'behave' correctly when correlated with interpersonal circle variables (i.e., convergent validity and discriminant validity). In this fashion, construct validity can be assessed by determining whether a particular personality variable correlates, or doesn't correlate, as predicted with the interpersonal variables (Gurtman, 1992). For example, a variable that is presumed to have a significant interpersonal component, such as extraversion, would be expected to demonstrate a circular pattern of correlations with scales measuring the interpersonal circle. A variable not expected to show this relationship (e.g., intelligence) should not correlate circularly with the interpersonal circle variables.
In addition to the study of individual characteristics from an interpersonal perspective, the circumplex model is especially useful in testing tenets of interpersonal theory itself. These principles are discussed elsewhere on this web site and the importance of the circumplex in studying them is clarified.