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.