Multiple Group Structural Equation Modeling of the Social Relations Model

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.

社会关系模型（Social Relations Model）是一类可将群体动态分析为个体间二元互动的统计工具。在多组结构方程模型框架下，本文提出以沃尔德检验（Wald test）与似然比检验（likelihood ratio test）为核心的组间比较方法，这两类检验分别基于（1）模型参数间的等式约束，以及（2）针对非线性参数变换限制的拉格朗日乘数检验，可用于对具有不同解读视角的各类群体动态量化方式开展组间对比。本文通过一则实证案例对所提方法进行演示验证。一项模拟研究考察了上述方法在I类错误率可恢复性与统计功效方面的表现，结果显示其整体性能颇具应用前景。最后本文讨论了该方法的应用启示与局限性。