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.