Considering Statistically Equivalent Models when using Structural Equation Modeling: an Example from Physics Identity

Structural equation modeling (SEM) is a statistical method widely used in educational research to investigate relationships between variables. Using a SEM model involves a crucial step of considering statistically equivalent models and contemplating why the proposed model should not be rejected in favor of equivalent ones. However, many studies using SEM did not explicitly discuss this step. In this study, we use physics identity model as an example to demonstrate how multiple statistically equivalent models have distinct instructional implications. Previous research has indicated that physics identity comprises three dimensions: perceived recognition, self-efficacy, and interest. However, the relationships between these dimensions have not been thoroughly understood. Here, we discuss how our proposed model with perceived recognition predicting self-efficacy and interest is supported by prior studies involving individual student interviews and how intervention studies can further determine a more accurate causal model. Our study highlights the importance of considering statistically equivalent models when using SEM as an analysis tool.