Testing Piecewise Structural Equations Models in the Presence of Latent Variables and Including Correlated Errors

ABSTRACT

Path models, expressed as Directed Acyclic Graphs (DAGs), and the testing of such DAGs via a d-sep test, have become popular because they can incorporate complicated data structures that are difficult or impossible to accommodate in classical structural equation modeling. However, d-sep tests cannot accommodate DAGs that include unmeasured (latent) variables. We describe (i) how to convert a DAG with latent variables into an observationally equivalent graph without latents (a Mixed Acyclic Graph, MAG), (ii) how this MAG identifies which latents can/cannot be ignored without changing the causal meaning of the original DAG, and (iii) how to perform the MAG equivalent of a d-sep test.

KEYWORDS:

• Causal hypothesis
• correlated errors
• d-separation
• d-sep tests
• latent variables
• m-separation
• m-sep test
• mixed graphs
• structural causal modeling

Acknowledgments

Clark Glymour, Françoise Cardou, Li Zhang and two anonymous reviewers provided helpful comments on this paper. This research was financially supported by an NSERC Discovery Grant to BS.