Multilevel testing of constraints induced by structural equation modeling in fMRI effective connectivity analysis: A proof of concept

In functional MRI (fMRI), effective connectivity analysis aims at inferring the causal influences that brain regions exert on one another. A common method for this type of analysis is structural equation modeling (SEM). We here propose a novel method to test the validity of a given model of structural equation. Given a structural model in the form of a directed graph, the method extracts the set of all constraints of conditional independence induced by the absence of links between pairs of regions in the model and tests for their validity in a Bayesian framework, either individually (constraint by constraint), jointly (e.g., by gathering all constraints associated with a given missing link), or globally (i.e., all constraints associated with the structural model). This approach has two main advantages. First, it only tests what is testable from observational data and does allow for false causal interpretation. Second, it makes it possible to test each constraint (or group of constraints) separately and, therefore, quantify in what measure each constraint (or, e..g., missing link) is respected in the data. We validate our approach using a simulation study and illustrate its potential benefits through the reanalysis of published data.