What are the inner and outer models in SEM?

In a structural equation modeling (SEM) analysis, the inner model is the part of the model that describes the relationships among the latent variables that make up the model. The outer model is the part of the model that describes the relationships among the latent variables and their indicators.

In this sense, the path coefficients are inner model parameter estimates. The weights and loadings are outer model parameter estimates. The inner and outer models are also frequently referred to as the structural and measurement models, respectively.

More precisely, the mathematical equations that express the relationships among latent variables are referred to as the structural model. The equations that express the relationships among latent variables and indicators are referred to as the measurement model.

The term structural equation model is used to refer to both the structural and measurement model, combined.