The circumplex structure of affect: A Swedish version

The taxonomy of a circumplex model has been widely applied in the emotion domain and especially by researchers advocating a systematic arrangement of conscious emotional experience (see Fabrigar, Visser & Browne, 1997; Feldman Barett & Russell, 1999 for recent reviews). To rule out some of the lexical problems in the naming of affective states in the circumplex space, Larsen and Diener (1992) suggested a labeling system with forty-eight English adjectives representing eight affective states. The objective of the present study was to examine how well Swedish adjectives map onto a dimensional model of this kind, in doing so, to compose a Swedish measure for self-reported affect. The forty-eight Swedish adjectives translated from Larsen and Diener (1992) failed to capture a pure circumplex structure. However, when approximately two thirds of these adjectives were reanalyzed, a reasonable consistency with the circumplex model was reached. This suggested a composite Swedish measure for self-rated affect, with up to four adjectives representing each of the eight affective states in the circumplex space.     

Evaluation of the circumplex structure of the Activation Deactivation Adjective Check List before and after a short walk

Background and purpose: The Activation Deactivation Adjective Check List (AD ACL; Thayer, 1989, The biopsychology of mood and arousal. New York: Oxford University Press) has been used in several studies to assess affective responses to bouts of physical activity. In recent years, researchers have suggested that the structure of this multidimensional measure should approximate a circumplex. This hypothesis was examined using a circumplex-specific confirmatory method.Methods: Volunteers (n=165) completed the AD ACL before and after a short walk. The data were analyzed using Browne’s Circumplex models for correlation matrices. (Psychometrika, 57, 469–497) circular stochastic process model and CIRCUM software and the analyses were performed at the item level.Results and conclusions: Before the walk, the circumplex provided a close fit to the data, whereas, after the walk, the fit was lower, but still reasonable. At neither time did items theorized to belong to one subscale become interspersed with items theorized to belong to an adjacent subscale. The AD ACL represents a satisfactory, albeit imperfect, option for the assessment of affective responses to physical activity from a circumplex perspective. In the future, closer fit to circumplex structure should be achieved by taking the specific structural postulates of the circumplex model into account from the beginning of the scale development process.     

A Simple, Exact Test for the Holland Hexagon

A method is presented for testing the full circumplex model implied by Holland's (1992) theory of vocational interests. The procedure is based on the Spearman rank-order correlation coefficient applied to the hypothesized ranks among correlations defined by the hexagon. In keeping with Holland's stated preference for simple measures and techniques (Holland, 1992, pp. 6–7), the method is easy to compute and apply and, unlike existing techniques, is readily amenable to comparing the fit found in several matrices and for use in meta-analysis.     

On the broad applicability of the affective circumplex: representations of affective knowledge among schizophrenia patients

Abstract - Studies of affective experience are guided by the assumption that the structure of affect generalizes across people. Yet this assumption has not been tested among educationally and economically diverse community residents or among individuals with psychopathology. This study explicitly examined the broad applicability of the valence-arousal circumplex and whether schizophrenia patients and nonpatients have comparable knowledge structures of affective phenomena. Patients and nonpatients completed similarity ratings of 120 pairs of affect words. Similarity judgments were analyzed separately for each group using a multidimensional scaling procedure, and solutions were compared. Results revealed the same two-dimensional valence-arousal solution for schizophrenia patients and nonpatients, although there were subtle differences between the groups. These findings provide additional evidence that the circumplex model is a useful formalism for representing affective phenomena across diverse populations, and they bolster confidence in existing interpretations of schizophrenia patients' reports of affective experience.     

Structural examination of RIASEC scales in high school students: Variation across ethnicity and method

The structural validity of Holland’s model of vocational interests across racial/ethnic groups was examined in the population of high school juniors in two states. The fit of the circumplex model to Holland’s RIASEC types as assessed by the UNIACT-R was evaluated for the general sample and five subgroups: Caucasian/Euro-Americans, African Americans, Asian Americans, Latinos, and Native Americans. Four different methods were used to test the proposed circumplex structure, each with various circumplex definitions. Results indicate that nonparametric methods generally showed good model-data fit, whereas SEM-based results indicated less support. No differences in fit were found across ethnicity supporting the usage with U.S. ethnic groups.     

A Rigorous Test of the Fit of the Circumplex Model to Big Five Personality Data: Theoretical and Methodological Issues and Two Large Sample Empirical Tests

Our objective was to apply the rigorous test developed by Browne (1992) to determine whether the circumplex model fits Big Five personality data. This test has yet to be applied to personality data. Another objective was to determine whether blended items explained correlations among the Big Five traits. We used two working adult samples, the Eugene-Springfield Community Sample and the Professional Worker Career Experience Survey. Fit to the circumplex was tested via Browne's (1992) procedure. Circumplexes were graphed to identify items with loadings on multiple traits (blended items), and to determine whether removing these items changed five-factor model (FFM) trait intercorrelations. In both samples, the circumplex structure fit the FFM traits well. Each sample had items with dual-factor loadings (8 items in the first sample, 21 in the second). Removing blended items had little effect on construct-level intercorrelations among FFM traits. We conclude that rigorous tests show that the fit of personality data to the circumplex model is good. This finding means the circumplex model is competitive with the factor model in understanding the organization of personality traits. The circumplex structure also provides a theoretically and empirically sound rationale for evaluating intercorrelations among FFM traits. Even after eliminating blended items, FFM personality traits remained correlated.     

Integrating covariates into circumplex structures: an extension procedure for Browne’s circular stochastic process model

Circumplex structures are elements of various psychological domains. Most work focuses on assessing the circular ordering of circumplex indicators and their relationships with covariates. In this article, an extension procedure for Browne’s circumplex model is presented. Our approach models the relationships among circumplex indicators and the relationships of covariates with a latent circumplex simultaneously without affecting the circumplex indicators’ positions on the circumplex. The approach builds upon Browne’s Fourier series parameterization of a correlation function, which is used to model the latent circumplex correlation structure. It extends the shape of the correlation function to the profile of each covariate’s correlations with the circumplex. The model is specified in the framework of structural equation modeling, thereby making it possible to test various hypotheses. Procedures are presented for deriving interval estimates for the parameters that relate the covariates to the circumplex. The model is compared to other approaches for assessing the relationships of a circumplex with covariates. The results of the exemplary applications and a simulation study were in favor of the suggested model. The approach is furthermore illustrated with a real-data example, focusing on the relationships between the interpersonal circumplex and the rivalry and admiration aspects of narcissism.     

Further Support for a Hierarchical Model of Affect: Reply to Green and Salovey

Green and Salovey agree with us that happiness and sadness are strongly bipolar, and that Positive and Negative Activation are not. However, Green and Salovey subscribe to the two-dimensional circumplex, a model we find wanting. Actually, the problems they discuss arise from the limitations of the circumplex rather than from issues fundamental to affective structure. And they do not consider the evidence, reported in our target article, that supports an alternative to the circumplex: a three-level hierarchical model. In this reply, we take a closer look at the empirical findings supporting this model, and we emphasize its heuristic promise.     

Analysis of the affect measurement conundrum in exercise psychology: IV. A conceptual case for the affect circumplex

Background and purpose: In previous articles in this 4-part series, we presented an analysis of some of the main problems surrounding the measurement of affect in exercise psychology. The purpose of the present paper is to integrate this experience into a proposed solution by presenting arguments in support of the circumplex model of affect.Methods: The circumplex model is considered a suitable solution because (a) it targets the broadest concept in the affective hierarchy, namely basic affect, (b) as a dimensional model, it offers unparalleled breadth of scope and parsimony, (c) it is domain-general, thus not likely to produce assessments that are biased against or in favor of a certain treatment, and (d) it is based on specific conceptual postulates, thus allowing a deductive approach to measurement. The basic assumptions of the circumplex model are discussed, the available circumplex-based self-report measures are reviewed, and a series of applied studies in the context of acute exercise are summarized.Results and conclusions: Two important caveats are emphasized: (a) the measurement of the circumplex dimensions presents certain unique challenges which advances in statistical modeling should soon address and (b) the circumplex should not be seen as a panacea for all types of research contexts as its strength lies mainly in its parsimony, not its specificity. Provided that these points are taken into consideration, the circumplex model can offer a useful framework for conceptualizing and assessing the effects of acute exercise on the affective domain.     

Individual difference variables,affective differentiation,and the structures of affect

Methodological arguments are usually invoked to explain variations in the structure of affect. Using self-rated affect from Italian samples (N=600), we show that individual difference variables related to affective differentiation can moderate the observed structure. Indices of circumplexity and congruence coefficients to the hypothesized target were used to quantify the observed structures. Results did not support the circumplex model as a universal structure. A circular structure with axes of activation and valence was approximated only among more affectively differentiated groups: students and respondents with high scores on Openness to Feelings and measures of negative emotionality. A different structure, with unipolar Positive Affect and Negative Affect factors, was observed among adults and respondents with low Openness to Feelings and negative emotionality. The observed structure of affect will depend in part on the nature of the sample studied.     

Studying Affect Among the Chinese: The Circular Way

Past research on Chinese emotion has been plagued by the lack of a measurement map for affective feelings. In this article, I developed a fine-grained circumplex model of affective feelings that is arbitrarily defined by 12 segments. I created twelve 4-item self-report scales to measure affect felt during a clearly remembered moment (N = 395), and I cross-validated them twice with affect felt during the current moment (Ns = 269, 302). The structural and psychometric properties of these scales were strongly supported. The CIRCUM-extension procedure (M. Browne, personal communication, June 12, 1999) that places external correlates into the affective space showed that 28 of 28 mood states and 6 of 13 traits were significantly related to affect. External correlates did not clarify which of the affect dimensions were basic. The newly developed scales will serve as a useful tool in assessing affect among Chinese people and as a platform on which to extend the nomological net of affect.     

Circumplex models for correlation matrices

Structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed. Particular attention is given to a stochastic process defined on the circle proposed by T. W. Anderson. It is shown that the Anderson circumplex contains the Markov Process model for a simplex as a limiting case when a parameter tends to infinity.Anderson's model is intended for correlation matrices with positive elements. A replacement for Anderson's correlation function that permits negative correlations is suggested. It is shown that the resulting model may be reparametrzed as a factor analysis model with nonlinear constraints on the factor loadings. An unrestricted factor analysis, followed by an appropriate rotation, is employed to obtain parameter estimates. These estimates may be used as initial approximations in an iterative procedure to obtain minimum discrepancy estimates.Practical applications are reported.Presented as the 1992 Psychometric Society Presidential Address. I am greatly indebted to Stephen Du Toit for help in the development of the computer program employed here. Part of this research was carried out at the University of South Africa and at the Institute for Statistical Research of the South African Human Sciences Research Council.     

In What Sense Are Positive and Negative Affect Independent?

We agree with most of the claims made by Tellegen, Watson, and Clark: Pleasant and unpleasant affect (i.e., happiness and unhappiness) are strongly negatively correlated; random and nonrandom error need to be taken into account before interpreting correlations among affect scales; scales of positive affect (PA) and negative affect (NA) embedded within the affective circumplex are orthogonal in theory, as are pleasure and arousal; and two-dimensional views of the affective space are more valid and useful than one- or three- dimensional models. Finally, and most important, we agree that PA and NA, as typically operationalized, are not independent, despite what may be the case theoretically. In this brief rejoinder, we offer some reasons why measurement problems likely prevent PA and NA from being measured orthogonally, why the factor analytic work reported in the target article is unlikely to shed new light on the perplexing problem of how best to characterize and measure affect, and why Pleasantness and Arousal tend to be operationally superior to their PA and NA counterparts.     

The fractal property of internal structure of facial affect recognition: A complex system approach

Based on a circumplex model of facial affect, four inner affective circumplexes, assumed to have 100%, 75%, 50%, and 25% emotional intensities, were investigated in terms of fractal, which is a concept of complex systems. Results revealed that the perimeters of the circumplex excluding the 25% condition possessed fractal property characterised by features specific to fractals. Results also showed that fractal dimension in the 50% condition (1.58 dimension) was significantly higher than that in the 100% (1.45 dimension) and 75% (1.45 dimension) conditions, indicating that the cognitive structure of facial affect in the 50% condition was more complex than that in the 100% and 75% conditions.     

An Idiographic Examination of Day-to-Day Patterns of Substance Use Craving,Negative Affect,and Tobacco Use Among Young Adults in Recovery

Psychological constructs, such as negative affect and substance use cravings that closely predict relapse, show substantial intraindividual day-to-day variability. This intraindividual variability of relevant psychological states combined with the “one day at a time” nature of sustained abstinence warrant a day-to-day investigation of substance use recovery. This study examines day-to-day associations among substance use cravings, negative affect, and tobacco use among 30 college students in 12-step recovery from drug and alcohol addictions. To account for individual variability in day-to-day process, it applies an idiographic approach. The sample of 20 males and 10 females (mean age = 21) was drawn from members of a collegiate recovery community at a large university. Data were collected with end-of-day data collections taking place over an average of 26.7 days. First-order vector autoregression models were fit to each individual predicting daily levels of substance use cravings, negative affect, and tobacco use from the same 3 variables 1 day prior. Individual model results demonstrated substantial interindividual differences in intraindividual recovery process. Based on estimates from individual models, cluster analyses were used to group individuals into 2 homogeneous subgroups. Group comparisons demonstrate distinct patterns in the day-to-day associations among substance use cravings, negative affect, and tobacco use, suggesting the importance of idiographic approaches to recovery management and that the potential value of focusing on negative affect or tobacco use as prevention targets depends on idiosyncratic processes.     

Examining the Invariance of Holland's Vocational Interest Model across Gender

This study examines the structural invariance of Holland's (1973, 1985) vocational interest model across gender. Evidence of gender differences in the fit of Holland's model was sought by submitting 14 (7 male; 7 female) previously published Strong Interest Inventory (SII) General Occupational Themes (GOT) scale correlation matrices to multiple structural analytic techniques. Randomization tests of hypothesized order relations (Hubert Arabie, 1987) and single sample confirmatory factor analyses (CFA) indicated a moderate to strong correspondence between GOT data and Holland's circular order and circumplex models. Randomization tests of differences in model–data fit, and two-sample CFA indicated that these models are a no more or less accurate representation of the observed data for men than for women. Additional analyses aimed at identifying gender differences in the misfit of specific aspects of Holland's model also yielded no evidence of differential fit.     

The Structure of Current Affect: Controversies and Emerging Consensus

For some years now, emotion researchers have debated a series of issues related to the structure of consciously experienced affective states. The present article reviews evidence that current affective experience can be summarized by a structure that is anchored by two bipolar but independent dimensions of experience, pleasure and activation. Four issues have presented themselves as central to the nature of this structure: the number of dimensions necessary to describe the space, the bipolarity of the dimensions, whether the structure displays a circumplex shape, and the definition of the activation dimension. Points of consensus and the remaining controversies regarding each issue are presented.     

Discrete Emotions or Dimensions? The Role of Valence Focus and Arousal Focus

The present study provides evidence that valence focus and arousal focus are important processes in determining whether a dimensional or a discrete emotion model best captures how people label their affective states. Individuals high in valence focus and low in arousal focus fit a dimensional model better in that they reported more co-occurrences among like-valenced affective states, whereas those lower in valence focus and higher in arousal focus fit a discrete model better in that they reported fewer co-occurrences between like-valenced affective states. Taken together, these findings suggest that one static, nomothetic theory may not accurately describe the subjective affective experience of all individuals.     

Subordinate Influence and the Performance Evaluation Process: Test of a Model

A causal model of the performance evaluation process was proposed and tested in this paper. The proposed conceptualization incorporated social, situational, affective, and cognitive elements as they affect performance ratings, with particular emphasis on the role of subordinate influence behaviors. LISREL results demonstrated that the proposed model fit the data well, and reflected a better fit than several alternative models that were estimated. The contributions and limitations of the present study were discussed, in addition to challenges and directions for future research.     

A note on structural models for the circumplex

Jöreskog (1974) developed a latent variable model for the covariance structure of the circumplex which, under certain conditions, includes a model for a patterned correlation matrix (Browne, 1977). This model is of limited usefulness, however, in that it employs a known matrix that is rank deficient for many problems. Furthermore, the model is inappropriate for the circumplex which contains negative covariances. This paper presents alternative models for the perfect circumplex and quasi-circumplex that avoids these difficulties, and that includes the important model for a patterned correlation circumplex matrix. Two numerical examples are provided.This research was supported in part by a grant from the Graduate School of the University of Minnesota. I wish to thank M. W. Browne for suggesting the final model presented in this paper. James Steiger and the Editor also made several valuable suggestions.