Multiple Group Structural Equation Modeling of the Social Relations Model

Abstract

The social relations model is a statistical tool that allows the analysis of group dynamics as dyadic interactions between individuals. Within a multiple group structural equation modeling framework, Wald-tests and likelihood ratio tests based on (1) equality constraints among model parameters and (2) Lagrange multipliers for restrictions among non-linear parameter transformations are presented as methods for group-comparisons of various quantifications of group dynamics that hold different interpretations. The methods are illustrated with an empirical example. A simulation study investigates the performance of the methods with regard to Type I error-rate recoverability and statistical power and displays overall promising results. Implications and limitations are discussed.

Keywords:

• Dyadic data
• group dynamics
• Lagrange-multiplier
• multiple groups
• social relations model

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Correction

Acknowledgments

We would like to thank Johanna Eiben for her help during the literature review for this article.

Disclosure Statement

We have no conflict of interest to disclose. The research for this article was not funded by external sources. Figure 1 was reproduced and altered from a different manuscript written by the author that is currently under review. The Open Access data used in this article for illustration purposes was retrieved from http://davidakenny.net/srm/srmdata.htm (data-name: “Zero”) and written permission to use it was inquired from David A. Kenny via email. The data is provided in the supplemental material to this article.

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/10705511.2022.2123641)

Notes

1 Such a research-question might seem far-fetched. However, we deemed it appropriate for illustration purposes because a real data application is more interesting than the analysis of simulated data and because we can check whether such a weakly constructed hypothesis will actually be met with lack of evidence. More useful examples for the employment of the approach will be given in the remainder.

2 We note that a difference of SRM-parameters between a control and a treatment-group can only be interpreted as a causal effect resulting from the treatment if certain requirements are met. We will elaborate on this in the discussion.