, Volume 82, Issue 4, pp 1162–1181 | Cite as

Tackling Longitudinal Round-Robin Data: A Social Relations Growth Model

  • Steffen NestlerEmail author
  • Katharina Geukes
  • Roos Hutteman
  • Mitja D. Back


The social relations model (SRM) is commonly used in the analysis of interpersonal judgments and behaviors that arise in groups. The SRM was developed only for use with cross-sectional data. Here, we introduce an extension of the SRM to longitudinal data. The social relations growth model represents a person’s repeated SRM judgments of another person as a function of time. We show how the model’s parameters can be estimated using restricted maximum likelihood, and how the effects of covariates on interindividual and interdyad variability in growth can be computed. An example is presented to illustrate the suggested approach. We also present the results of a small simulation study showing the suitability of the social relations growth model for the analysis of longitudinal SRM data.


social relations model linear mixed model longitudinal data restricted maximum likelihood 



We are grateful to Sarah Humberg for very helpful comments on an earlier version of the manuscript.


  1. Ackerman, R. A., Kashy, D. A., Donellan, M. B., & Conger, R. D. (2011). Positive engagement behaviors in observed family iinteractions: A social relations perspective. Journal of Family Psychology, 25, 719–730.CrossRefPubMedPubMedCentralGoogle Scholar
  2. Bates, D., Maechler, M., Bolker, B. M., & Walker, S. (2014). Lme4: Linear mixed effects models using eigen und s4. Retrieved from
  3. Bond, C. F., Dorsky, S. E., & Kenny, D. A. (1992). Person memory and memorability: A round robin analysis. Basic and Applied Social Psychology, 13, 285–302.CrossRefGoogle Scholar
  4. Bond, C. F., Horn, E. M., & Kenny, D. A. (1997). A model for triadic relations. Psychological Methods, 2, 79–94.CrossRefGoogle Scholar
  5. Bond, C. F., & Lashley, B. R. (1996). Round-robin analysis of social interaction: Exact and estimated standard errors. Psychometrika, 61, 303–311.CrossRefGoogle Scholar
  6. Bonito, J. A., & Kenny, D. A. (2010). The measurement of reliability of social relations components from round-robin designs. Personal Relationships, 17, 235–251.CrossRefGoogle Scholar
  7. Branje, S. J. T., Finkenauer, C., & Meeus, W. H. J. (2008). Modeling interdependent data in developmental psychology. In N. Card, J. Selig, & T. Little (Eds.), Modeling interdependent data in developmental psychology (pp. 287–317). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  8. Branje, S. J. T., van Lieshout, C. F. M., & van Aken, M. A. G. (2005). Relations between agreeableness and perceived support in family relationships: Why nice people are not always supportive. International Journal of Behavioral Development, 29, 120–128.CrossRefGoogle Scholar
  9. Buist, K. L., Reitz, E., & Dekovic, M. (2008). Attachment stability and change during adolescence: A longitudinal application of the social relations model. Journal of Social and Personal Relationships, 25, 429–444.CrossRefGoogle Scholar
  10. Card, N. A., Little, T. D., & Selig, J. P. (2008). Using the bivariate social relations model to study dyadic relationships: Early adolescents’ perceptions of friends’ aggression and prosocial behavior. In N. A. Card, J. P. Selig, & T. D. Little (Eds.), Modeling dyadic and interdependent data in the developmental and behavioral sciences (pp. 245–276). New York: Routledge.Google Scholar
  11. Cook, W. L. (2008). Application of the social relations model formulas to developmental research. In N. A. Card, J. P. Selig, & T. D. Little (Eds.), Modeling dyadic and interdependent data in the developmental and behavioral sciences (pp. 245–276). New York: Routledge.Google Scholar
  12. Curran, P. J., & Bollen, K. A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change. Decade of behavior (pp. 107–135). Washington, DC: APA.CrossRefGoogle Scholar
  13. Demidenko, E. (2004). Mixed models: Theory and applications with R (2nd ed.). Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  14. Dorff, C., & Ward, M. D. (2013). Networks, dyads, and the social relations model. Political Science Research Methods, 1, 159–178.CrossRefGoogle Scholar
  15. Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., & Hothorn, T. (2016). mvtnorm: Multivariate Normal and t Distributions. R package version 1.0–5.
  16. Geukes, K., Hutteman, R., Küfner, A., Nestler, S., & Back, M. D. (2016). Explaining the longitudinal interplay of personality and social relationships in the laboratory and in the field: The PILS and the CONNECT study. Manuscript in preparation.Google Scholar
  17. Gill, P. S., & Swartz, T. B. (2001). Statistical analyses for round robin interaction data. Canadian Journal of Statistics, 29, 321–331.CrossRefGoogle Scholar
  18. Gill, P. S., & Swartz, T. B. (2007). Bayesian analysis of dyadic data. American Journal of Mathematical and Managment Sciences, 27, 73–92.Google Scholar
  19. Hoff, P. D. (2005). Bilinear mixed-effects models for dyadic data. Journal of the American Statistical Association, 100, 286–295.CrossRefGoogle Scholar
  20. Horn, E. M., Collier, W. G., Oxford, J. A., Bond, C. F., & Dansereau, D. F. (1998). Individual differences in dyadic cooperative learning. Journal of Educational Psychology, 90, 153–161.CrossRefGoogle Scholar
  21. Jiang, J. (2007). Linear and generalized linear mixed models and their applications. New York: Springer.Google Scholar
  22. Kenny, D. A. (1994). Interpersonal perception: A social relations analysis. New York: Guilford Press.Google Scholar
  23. Kenny, D. A. (2004). PERSON: A general model of interpersonal perception. Personality and Social Psychology Review, 8, 265–280.CrossRefPubMedGoogle Scholar
  24. Kenny, D. A., Kashy, D. A., & Cook, W. L. (2006). The analysis of dyadic data. New York: Guilford Press.Google Scholar
  25. Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electornic Journal of Statistics, 6, 1100–1128.CrossRefGoogle Scholar
  26. Küfner, A. C. P., Nestler, S., & Back, M. D. (2012). The two pathways to being an (un-)popular narcissist. Journal of Personality, 81, 184–195.CrossRefGoogle Scholar
  27. Leckelt, M., Küfner, A. C. P., Nestler, S., & Back, M. D. (2015). Behavioral processes underlying narcissist’s decline in popularity. Journal of Personality and Social Psychology, 109, 856–871.CrossRefPubMedGoogle Scholar
  28. LeDoux, J. A., Gorman, C. A., & Woehr, D. J. (2012). The impact of interpersonal perceptions on team processes: A social relations analysis. Small Group Research, 43, 356–382.CrossRefGoogle Scholar
  29. Lüdtke, O., Robitzsch, A., Kenny, D. A., & Trautwein, U. (2013). A general and flexible approach to estimating the social relations model using Bayesian methods. Psychological Methods, 18, 101–119.CrossRefPubMedGoogle Scholar
  30. Lusher, D., Koskinen, J., & Robins, G. (2013). Exponential random graph models for social networks: Theories, methods and applications. New York: Cambridge University Press.Google Scholar
  31. Marcus, D. K., & Kashy, D. A. (1995). The social relations model: A tool for group psychotherapy research. Journal of Counseling Psychology, 42, 383–389.CrossRefGoogle Scholar
  32. McCulloch, C. E., Searle, S. R., & Neuhaus, J. M. (2004). Generalized, linear, and mixed models (2nd ed.). Hoboken, NJ: Wiley.Google Scholar
  33. Nestler, S. (2015). Restricted maximum likelihood estimation for parameters of the social relations model. Psychometrika. doi: 10.1007/s11336-015-9474-9.
  34. Nestler, S. (2016). Likelihood estimation of the multivariate social relations model. Psychometrika (in press).Google Scholar
  35. Nestler, S., Grimm, K. J., & Schönbrodt, F. D. (2015). The social consequences and mechanisms of personality: How to analyse longitudinal data from individual, dyadic, round-robin and network designs. European Journal of Personality, 29, 272–295.CrossRefGoogle Scholar
  36. Park, B., & Flink, C. (1989). A social relations analysis of agreement in liking judgments. Journal of Personality and Social Psychology, 56, 506–518.CrossRefGoogle Scholar
  37. Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36.CrossRefGoogle Scholar
  38. Schönbrodt, F. D., Back, M. D., & Schmukle, S. C. (2012). TripleR: An R package for social relations analyses based on round-robin designs. Behavior Research Methods, 44, 455–470. doi: 10.3758/s13428-011-0150-4.
  39. Schönbrodt, F. D., Back, M. D., & Schmukle, S. C. (2016). TripleR: Social Relation Model (SRM) analyses for single or multiple groups (R package version 1.5.1). Retrieved from
  40. Snijders, T. A. B., & Kenny, D. A. (1999). The social relations model for family data: A multilevel approach. Personal Relationships, 6, 471–486.CrossRefGoogle Scholar
  41. Snijders, T. A. B., Steglich, C. E. G., & van de Bunt, G. G. (2010). Introduction to actor-based models for network dynamics. Social Networks, 32, 44–60.CrossRefGoogle Scholar
  42. van Zalk, M. H., & Denissen, J. (2015). Idiosyncratic versus social consensus approaches to personality: Self-view, perceived, and peer-review similarity. Journal of Personality and Social Psychology, 109, 121–141.CrossRefPubMedGoogle Scholar
  43. Verbeke, G., Fieuws, S., Molenbergh, G., & Davidian, M. (2014). The analysis of multivariate longitudinal data: A review. Statistical Methods in Medical Research, 23, 42–59.CrossRefPubMedGoogle Scholar
  44. Verbeke, G., & Molenberghs, G. (2009). Linear mixed models for longitudinal data. Berlin: Springer.Google Scholar
  45. Warner, R. M., Kenny, D. A., & Stoto, M. (1979). A new round robin analysis of variance for social interaction data. Journal of Personality and Social Psychology, 37, 1742–1757.CrossRefGoogle Scholar
  46. Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. New York: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© The Psychometric Society 2016

Authors and Affiliations

  • Steffen Nestler
    • 1
    Email author
  • Katharina Geukes
    • 2
  • Roos Hutteman
    • 3
  • Mitja D. Back
    • 2
  1. 1.University of LeipzigLeipzigGermany
  2. 2.University of MünsterMünsterGermany
  3. 3.University of UtrechtUtrechtThe Netherlands

Personalised recommendations