Graphical Displays for Understanding SEM Model Similarity

Relationships between structural equation models are almost exclusively characterized as categorical. However, a simple yes–no answer as to whether 2 models are equivalent or nested (or other categorical descriptors of relationships) cannot address whether the models tend to fit similarly across a wide range of data, or how the characteristics of models and data affect the differences in fit. Therefore, such simple answers have limited value for model selection and evaluation. In this article we proposed a quantitative framework that allows for graphical display of results, incorporates the categorical distinctions in model similarity, is applicable to any model pairs, and offers a new method to generate data for studying model similarity. The framework is straightforward to implement and does not require complex analyses. The information this framework provides is diagnostic and can help researchers identify and explain how key characteristics in data and model parameters lead to (dis)similarity in fit.