Abstract
We present a confirmatory factor analysis (CFA) procedure for computing the reliability of circumplex axes. The tau-equivalent CFA variance decomposition model estimates five variance components: general factor, axes, scale-specificity, block-specificity, and item-specificity. Only the axes variance component is used for reliability estimation. We apply the model to six circumplex types and 13 instruments assessing interpersonal and motivational constructs—Interpersonal Adjective List (IAL), Interpersonal Adjective Scales (revised; IAS-R), Inventory of Interpersonal Problems (IIP), Impact Messages Inventory (IMI), Circumplex Scales of Interpersonal Values (CSIV), Support Action Scale Circumplex (SAS-C), Interaction Problems With Animals (IPI-A), Team Role Circle (TRC), Competing Values Leadership Instrument (CV-LI), Love Styles, Organizational Culture Assessment Instrument (OCAI), Customer Orientation Circle (COC), and System for Multi-Level Observation of Groups (behavioral adjectives; SYMLOG)—in 17 German-speaking samples (29 subsamples, grouped by self-report, other report, and metaperception assessments). The general factor accounted for a proportion ranging from 1% to 48% of the item variance, the axes component for 2% to 30%; and scale specificity for 1% to 28%, respectively. Reliability estimates varied considerably from .13 to .92. An application of the Nunnally and Bernstein formula proposed by Markey, Markey, and Tinsley overestimated axes reliabilities in cases of large-scale specificities but otherwise works effectively. Contemporary circumplex evaluations such as Tracey’s RANDALL are sensitive to the ratio of the axes and scale-specificity components. In contrast, the proposed model isolates both components.
Highlights
In the field of personality psychology, the interpersonal circumplex (IPC) has long been recognized as a model for organizing interpersonal behaviors or traits along the axes of status and love
Participants were asked for other perception and in four cases for metaperceptions, which are prediction of one’s own image in others. Leaders predicted how they were perceived by their team members in the Competing Values Leadership Instrument (CV-LI), and service providers anticipated how Columns 5 to 9 in Table 3 report the resultant variance components of the circumplex items according to the respective confirmatory factor analysis (CFA) models of the 13 instruments and 29 subsamples
Gurtman and Pincus (2000) urged for the amount of variance accounted for by the axes of a circumplex: Wiggins et al (1981) argued that any model-testing procedure applied to the circumplex should be able to answer two questions about the set of test variables: “(1) How well do these variables conform to a circular model? and (2) How much of the observed covariance among these variables is accounted for by such a model? (p. 267)
Summary
In the field of personality psychology, the interpersonal circumplex (IPC) has long been recognized as a model for organizing interpersonal behaviors or traits along the axes of status (dominance) and love (affiliation; Wiggins, 1979, 2003). Circumplex models that date back to Wundt and James have dominated the dimensional assessment of emotions (Carney & Colvin, 2010; Russell, 1980). The structure of personal values (Schwartz, 1992), goals and aspirations (Grouzet et al, 2005), vocational interests (e.g., Holland & Gottfredson, 1992), group behavior, and values (Bales & Cohen, 1979) as well as organizational values and leadership roles (Quinn, 1988) make use of circumplex models. Authors adhering to the first approach evaluate the circumplex structure of the items or scales of a new instrument. Nagy, Marsh, Lüdtke, and Trautwein (2009)
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