  Structural equation modeling (SEM) is a statistical method widely used in
educational research to investigate relationships between variables. SEM models
are typically constructed based on theoretical foundations and assessed through
fit indices. However, a well-fitting SEM model alone is not sufficient to
verify the causal inferences underlying the proposed model, as there are
statistically equivalent models with distinct causal structures that equally
well fit the data. Therefore, it is crucial for researchers using SEM to
consider statistically equivalent models and to clarify why the proposed model
is more accurate than the equivalent ones. However, many SEM studies did not
explicitly address this important step, and no prior study in physics education
research has delved into potential methods for distinguishing statistically
equivalent models with differing causal structures. In this study, we use
physics identity model as an example to discuss the importance of considering
statistically equivalent models and how other data can help to distinguish
them. Previous research has identified three dimensions of physics identity:
perceived recognition, self-efficacy, and interest. However, the relationships
between these dimensions have not been thoroughly understood. In this paper, we
specify a model with perceived recognition predicting self-efficacy and
interest, which is inspired by individual interviews with students in physics
courses to make physics learning environments equitable and inclusive. We test
our model with fit indices and discuss its statistically equivalent models with
different causal inferences among perceived recognition, self-efficacy, and
interest. We then discuss potential experiments that could further empirically
test the causal inferences underlying the models, aiding the refinement to a
more accurate causal model for guiding educational improvements.
