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 a 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.

中文翻译：

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具有不同因果结构的统计等效模型：物理恒等式的一个例子

结构方程模型（SEM）是一种广泛应用于教育研究中的统计方法，用于研究变量之间的关系。 SEM 模型通常基于理论基础构建并通过拟合指数进行评估。然而，仅靠一个拟合良好的 SEM 模型不足以验证所提出模型的因果推论，因为存在具有不同因果结构的统计等效模型，同样可以很好地拟合数据。因此，对于使用 SEM 的研究人员来说，考虑统计等效模型并阐明为什么所提出的模型比等效模型更准确至关重要。然而，许多 SEM 研究并没有明确解决这一重要步骤，而且之前的物理教育研究也没有深入研究区分具有不同因果结构的统计等效模型的潜在方法。在本研究中，我们以物理恒等模型为例，讨论考虑统计等效模型的重要性以及其他数据如何帮助区分它们。先前的研究已经确定了物理学身份的三个维度：感知认知、自我效能和兴趣。然而，这些维度之间的关系尚未被彻底理解。在本文中，我们指定了一个具有预测自我效能和兴趣的感知识别模型，该模型的灵感来自于对物理课程学生的个人访谈，以使物理学习环境变得公平和包容。我们用拟合指数测试我们的模型，并讨论其统计等效模型，以及感知认知、自我效能和兴趣之间不同的因果推论。然后，我们讨论潜在的实验，这些实验可以进一步通过实证检验模型背后的因果推论，帮助完善更准确的因果模型来指导教育改进。