Round-robin Designs Research Articles

Latent Reciprocal Engagement and Accuracy Variables in Social Relations Structural Equation Modeling

The social relations model (SRM) is the standard approach for analyzing dyadic data stemming from round-robin designs. The model can be used to estimate correlation-coefficients that reflect the overall reciprocity or accuracy of judgements for individual and dyads on the sample- or population level. Within the social relations structural equation modeling framework and on the statistical grounding of stochastic measurement and classical test theory, we show how the multiple indicator SRM can be modified to capture inter-individual and inter-dyadic differences in reciprocal engagement or inter-individual differences in reciprocal accuracy. All models are illustrated on an open-access round-robin data set containing measures of mimicry, liking, and meta-liking (the belief to be liked). Results suggest that people who engage more strongly in reciprocal mimicry are liked more after an interaction with someone and that overestimating one’s own popularity is strongly associated with being liked less. Further applications, advantages and limitations of the models are discussed.

A correlated traits correlated (methods - 1) multitrait-multimethod model for augmented round-robin data.

We didactically derive a correlated traits correlated (methods - 1) [CTC(M - 1)] multitrait-multimethod (MTMM) model for dyadic round-robin data augmented by self-reports. The model is an extension of the CTC(M - 1) model for cross-classified data and can handle dependencies between raters and targets by including reciprocity covariance parameters that are inherent in augmented round-robin designs. It can be specified as a traditional structural equation model. We present the variance decomposition as well as consistency and reliability coefficients. Moreover, we explain how to evaluate fit of a CTC(M - 1) model for augmented round-robin data. In a simulation study, we explore the properties of the full information maximum likelihood estimation of the model. Model (mis)fit can be quite accurately detected with the test of not close fit and dynamic root mean square errors of approximation. Even with few small round-robin groups, relative parameter estimation bias and coverage rates are satisfactory, but several larger round-robin groups are needed to minimize relative parameter estimation inaccuracy. Further, neglecting the reciprocity covariance-structure of the augmented round-robin data does not severely bias the remaining parameter estimates. All analyses (including data, R scripts, and results) and the simulation study are provided in the Supporting Information. Implications and limitations are discussed.

When Forecasting Mutually Supportive Matches Will Be Practically Impossible

Forecasting which dyads will develop mutually supportive relationships is an important applied and basic research question. Applying psychometric theory to the design of forecasting studies shows that agreement between dyad members about their relationship (relational reciprocity) sets an upper limit for forecasting accuracy by determining the reliability of measurement. To test this, we estimated relational reciprocity in Study 1. Participants in seven samples (six student and one military; N = 504; Ndyads = 766) rated each other on support-related constructs in round-robin designs. Relational reciprocity was very low, undermining reliability. Formulas from psychometric theory predicted that forecasting supportive dyads would be practically impossible. To test this, we had participants in Study 2 complete a measure for matching dyads derived from recent theory. As predicted, supportive matches could not be forecast with acceptable precision. Theoretically, this falsifies some predictions of recent social-support theory. Practically, it remains unclear how to translate basic social-support research into effective interventions.

Envy mediates the relation between low academic self-esteem and hostile tendencies

In previous research, there has been little discussion about mediators or moderators that affect the negative relation between self-esteem and hostile tendencies. In the current article, we propose a model in which envy mediates that relation in the academic context. Across three studies, with correlational (N1=303), experimental (N2=76), and round-robin designs (N3=330), results revealed that academic self-esteem indirectly influenced hostile tendencies through envy. In Studies 2 and 3, the indirect effect was moderated by the performance context. Results suggest that individuals with low academic self-esteem may exhibit hostile tendencies because of feelings of envy, especially in highly competitive contexts. Findings are discussed with respect to theoretical implications for research on personality and interpersonal perceptions.

Idiosyncratic versus social consensus approaches to personality: Self-view, perceived, and peer-view similarity.

In the current studies, the authors examined how peers influence friendship choices through individuals' perceptions of similarity between their own and others' Big Five traits. Self-reported and peer-reported data were gathered from 3 independent samples using longitudinal round-robin designs. Peers' ratings of how similar 2 persons appeared in extraversion and agreeableness predicted friendship formation likelihood between these 2 persons in all samples. This association was mediated by perceived similarity. Furthermore, another mediation effect was found for similarity in interaction style: Persons who were viewed by peers as having similar extraversion and agreeableness levels became more similar in interaction styles. Thus, the current studies indicate that extraversion and agreeableness influence the emergence of social relationships through intrapersonal perceptions of similarity and interpersonal social interactions. We encourage researchers to look at specific similarity effects that influence interpersonal and intrapersonal processes to understand how relationships are formed.

TripleR: An R package for social relations analyses based on round-robin designs

In this article, we present TripleR, an R package for the calculation of social relations analyses (Kenny, 1994) based on round-robin designs. The scope of existing software solutions is ported to R and enhanced with previously unimplemented methods of significance testing in single groups (Lashley & Bond, 1997) and handling of missing values. The package requires only minimal knowledge of R, and results can be exported for subsequent analyses to other software packages. We demonstrate the use of TripleR with several didactic examples.

The measurement of reliability of social relations components from round-robin designs

The social relations model (SRM) is a useful tool for measuring relationship effects, defined as the unique perceptions or behaviors of 2 people. The sources of variance in SRM studies are persons (actors and partners), groups, and items; the relationship effect is defined as the actor–partner interaction. By removing variance because of persons and groups, a measure of a “pure” relationship effect is obtained. In this article, generalizability theory (G Theory) is applied to estimate the reliability of SRM components from round-robin data structures. Using G Theory, reliability formulas for actor, partner, group, and relationship are developed and interpretations for the reliability estimates are provided. The authors also discuss how these formulas can be used in both planning and interpreting results from relationship research.

Bias and standard error for social reciprocity measurements

The directional consistency and skew-symmetry statistics have been proposed as global measure of social reciprocity. Although both measures can be useful for quantifying social reciprocity, researchers need to know whether these estimators are biased in order properly to assess descriptive results. That is, if estimators are biased, researchers should compare actual values with expected values under the specified null hypothesis. Furthermore, standard errors are needed to enable suitable assessment of discrepancies between actual and expected values. This paper aims to derive some exact and approximate expressions in order to obtain bias and standard error values for both estimators for round-robin designs, although the results can also be extended to other reciprocal designs.

The relationship between displaying and perceiving nonverbal cues of affect: A meta-analysis to solve an old mystery.

The authors address the decades-old mystery of the association between individual differences in the expression and perception of nonverbal cues of affect. Prior theories predicted positive, negative, and zero correlations in performance-given empirical results ranging from r = -.80 to r = +.64. A meta-analysis of 40 effects showed a positive correlation for nonverbal behaviors elicited as intentional communication displays but zero for spontaneous, naturalistic, or a combination of display types. There was greater variation in the results of studies having round robin designs and analyzed with statistics that do not account for the interdependence of data. The authors discuss implications for theorists to distinguish emotional skills in terms of what people are capable of doing versus what people actually do.

Prospects for Applying the Social Relations Model to Person Perception

One of the most frustrating aspects of being a scientist is the lack of feedback. So often we have worked long and hard on a paper, and, after the paper is published, we never receive a letter or any real comment about it. We consider ourselves lucky if the paper receives an occasional citation from someone besides ourselves. For most of us to enjoy our work, we must rely on the intrinsic rewards of doing it. So I am extremely gratified that my book, Interpersonal Perception: A Social Relations Analysis, has received four reviews from a group of serious scholars. Many criticisms concern limitations that I have already addressed in the book's final chapter. This response more complements than criticizes the four reviews. My response is organized around whether the approach developed in my book will be applied by the next generation of researchers in person perception. First, background concerning the book's orientation to person perception is presented. Next considered is the potential integration of the approach within social cognition and reasons why researchers are reluctant to adopt the approach. Likely future research will be an investigation of moderators, and a preliminary discussion of these variables is presented. Also, the approach requires designs like round-robins. Because the need for such designs has been questioned, a defense of roundrobin designs is presented. Finally, a series of miscellaneous issues is reviewed.

Rank-One Round Robin Designs

Abstract A class of analysis of variance models is proposed for analyzing round robin interaction data, where the actor and partner effects of any member are linearly related, thus forcing the covariance matrix of these effects to have rank one. Such data arise frequently in applications, for instance, in sociometric studies on structures of social relationships. A factor analytic approach is proposed for studying these models. Statistical inference about the linear effects is discussed and a convergent algorithm is presented for obtaining the maximum likelihood estimates of the covariance components. A data set is analyzed using the methodology developed.

Round Robin Analysis of Variance via Maximum Likelihood

Abstract A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the EM algorithm is proposed for obtaining the maximum likelihood estimates of the covariance components. A balanced data set is analyzed using the methodology developed.

Round Robin Analysis of Variance Via Maximum Likelihood

Abstract A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the EM algorithm is proposed for obtaining the maximum likelihood estimates of the covariance components. A balanced data set is analyzed using the methodology developed.