# Can I use AIC for path models and non-path models?

I am testing competing hypotheses where one hypothesis contains a mediation effects that can be modeled using a path model. The other hypothesis does not include a mediation effect and therefore can be modeled using a simple linear regression. Both models will be run using the same dataset and will have the response variable (or exogenous variable in the path model's case). Therefore, I am wondering if it is appropriate to utilize AIC to compare/rank these models? The path model is being built using the piecewiseSEM package. I have read papers where they have used AIC selection for different path models but never a case when comparing a path model to a non-path model.

Any thoughts would be appreciated.

• Could you not formulate both models in the path-model nomenclature to make their AICs directly comparable? May 24, 2021 at 10:16
• Unfortunately, this doesn't work. When I run the non-mediation model with a basic glm the aic is 100+ . When the same glm is run inside the path-model the AIC goes to 6... May 24, 2021 at 14:02

Assuming your mediation model is of the form $$A \rightarrow B \rightarrow C$$ and $$A \rightarrow C$$, where $$C$$ is your dependent variable and $$B$$ is the mediator, then you can indeed run a "non-path" model. Simply break the mediation path and run the model $$A \rightarrow B$$ and $$A \rightarrow C$$. This is accomplished by setting the path coefficient from $$B$$ to $$C$$ to zero. This will give you comparable models to use for either $$AIC$$ comparison (using the same set of variables and the same data set), and it will also allow you to conduct a $$\chi^2$$ model comparison as well (as these are nested models).