Testing Piecewise Structural Equations Models in the Presence of Latent Variables and Including Correlated Errors
Bill Shipley, Jacob C. Douma
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.
Topics & Concepts
Directed acyclic graphLatent variableStructural equation modelingMixed graphCausal modelMoral graphPiecewiseMathematicsGraphComputer scienceAlgorithmDiscrete mathematicsStatisticsMathematical analysisLine graphVoltage graphBayesian Modeling and Causal InferenceAdvanced Graph Neural Networks