Abstract
The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM to an arbitrary number of variables and show how the parameters of this multivariate model can be estimated using a maximum likelihood or a restricted maximum likelihood approach. Overall, the two likelihood approaches provide consistent and efficient parameter estimates and can be used to investigate a multitude of interesting research questions.
References
|
Ackerman, R. A., Kashy, D. A., Donellan, M. B., Conger, R. D. (2011). Positive engagement behaviors in observed family interactions: A social relations perspective. Journal of Family Psychology, 25, 719–730. Google Scholar | Medline | |
|
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. Google Scholar | |
|
Bond, C. F., Lashley, B. R. (1996). Round-robin analysis of social interaction: Exact and estimated standard errors. Psychometrika, 61, 303–311. Google Scholar | |
|
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. Google Scholar | SAGE Journals | |
|
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. Google Scholar | SAGE Journals | |
|
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 Card, N. A., Selig, J. P., Little, T. D. (Eds.), Modeling dyadic and interdependent data in the developmental and behavioral sciences (pp. 245–276). New York, NY: Routledge Taylor & Francis. Google Scholar | |
|
Demidenko, E. (2004). Mixed models: Theory and applications with R (2nd ed.). Hoboken, NJ: John Wiley. Google Scholar | |
|
Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., Hothorn, T. (2017). Mvtnorm: Multivariate normal and t distributions. Retrieved from http://cran.r-project.org/web/packages/mvtnorm Google Scholar | |
|
Gill, P. S., Swartz, T. B. (2001). Statistical analyses for round robin interaction data. Canadian Journal of Statistics, 29, 321–331. Google Scholar | |
|
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. Google Scholar | |
|
Jiang, J. (2007). Linear and generalized linear mixed models and their applications. New York, NY: Springer. Google Scholar | |
|
Kenny, D. A. (1994). Interpersonal perception: A social relations analysis. New York, NY: Guilford Press. Google Scholar | |
|
Kenny, D. A. (2007). Estimation of SRM using specialized software. Storrs, CT: University of Connecticut. Google Scholar | |
|
Kenny, D. A., Albright, L., Malloy, T. E., Kashy, D. A. (1994). Consensus in interpersonal perception: Acquaintance and the big five. Psychological Bulletin, 116, 245–258. Google Scholar | Medline | |
|
Kenny, D. A., Kashy, D. A., Cook, W. L. (2006). The analysis of dyadic data. New York, NY: Guilford Press. Google Scholar | |
|
Kenny, D. A., Livi, S. (2009). A componential analysis of leadership using the social relations model. In Yammarino, F. J., Dansereau, F. (Eds.), Multi-level issues in organizational behavior and leadership (pp. 147–191). Bingley, England: Emerald. Google Scholar | |
|
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. Google Scholar | |
|
Lashley, B. R., Bond, C. F. (1997). Significance testing for round robin data. Psychological Methods, 2, 278–291. Google Scholar | |
|
Li, H. (2006). The covariance structure and likelihood function for multivariate dyadic data. Journal of Multivariate Analysis, 97, 1263–1271. Google Scholar | |
|
Li, H., Loken, E. (2002). A unified theory of statistical analysis and inference for variance component models for dyadic data. Statistica Sinica, 12, 519–535. Google Scholar | |
|
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. Google Scholar | Medline | |
|
McCulloch, C. E., Searle, S. R., Neuhaus, J. M. (2004). Generalized, linear, and mixed models. Hoboken, NJ: John Wiley. Google Scholar | |
|
Mehta, P. D. (2013). N-level structural equation modeling. In Petscher, Y., Schatschneider, C., Compton, D. L. (Eds.), Applied quantitative analysis in the social sciences (pp. 329–361). New York, NY: Routledge. Google Scholar | |
|
Nestler, S. (2016). Restricted maximum likelihood estimation for parameters of the social relations model. Psychometrika, 81, 1098–1117. Google Scholar | Medline | |
|
Nestler, S., Geukes, K., Hutteman, R., Back, M. D. (in press). Tackling longitudinal round-robin data: The social relations growth model. Psychometrika. Google Scholar | |
|
Pawitan, Y. (2001). In all likelihood: Statistical modelling and inference. Oxford, England: Oxford University Press. Google Scholar | |
|
R Core Team . (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org/ Google Scholar | |
|
Rabe-Hesketh, S., Skrondal, A. (2004). Generalized latent variable models. New York, NY: Chapman & Hall. Google Scholar | |
|
Schönbrodt, F. D., Back, M. D., Schmukle, S. C. (2017). TripleR: A package for round robin analyses using R. Retrieved from http://cran.r-project.org/web/packages/TripleR Google Scholar | |
|
Snijders, T. A. B., Kenny, D. A. (1999). The social relations model for family data: A multilevel approach. Personal Relationships, 6, 471–486. Google Scholar | |
|
Verbeke, G., Molenberghs, G. (2009). Linear mixed models for longitudinal data. Berlin, Germany: Springer. Google Scholar | |
|
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. Google Scholar |
