Data_Sheet_2_Probability-of-Superiority SEM (PS-SEM)—Detecting Probability-Based Multivariate Relationships in Behavioral Research.docx

In behavioral research, exploring bivariate relationships between variables X and Y based on the concept of probability-of-superiority (PS) has received increasing attention. Unlike the conventional, linear-based bivariate relationship (e.g., Pearson's correlation), PS defines that X and Y can be related based on their likelihood—e.g., a student who is above mean in SAT has 63% likelihood of achieving an above-mean college GPA. Despite its increasing attention, the concept of PS is restricted to a simple bivariate scenario (X-Y pair), which hinders the development and application of PS in popular multivariate modeling such as structural equation modeling (SEM). Therefore, this study addresses an empirical-based simulation study that explores the potential of detecting PS-based relationship in SEM, called PS-SEM. The simulation results showed that the proposed PS-SEM method can detect and identify PS-based when data follow PS-based relationships, thereby providing a useful method for researchers to explore PS-based SEM in their studies. Conclusions, implications, and future directions based on the findings are also discussed.

在行为研究领域，基于概率优势（PS）概念探究变量X与Y之间的双变量关系，这一研究方法已日益受到关注。与传统基于线性关系的双变量关系（如皮尔逊相关系数）不同，PS认为X与Y之间的关系可以基于其可能性——例如，SAT成绩高于平均分的学生有63%的可能性获得高于平均分的大学平均成绩。尽管该概念受到了越来越多的关注，但概率优势（PS）的概念仅限于简单的双变量场景（X-Y对），这阻碍了PS在结构方程模型（SEM）等流行多变量建模中的应用发展。因此，本研究针对基于实证的模拟研究，探讨在结构方程模型（SEM）中检测基于PS关系的潜力，称之为PS-SEM。模拟结果表明，所提出的PS-SEM方法能够检测并识别当数据遵循基于PS的关系时，从而为研究人员在研究中探索基于PS的SEM提供了一种有用的方法。此外，还讨论了基于研究发现的结论、启示和未来发展方向。