Using Partial Correlation to Enhance Structural Equation Modeling of Functional MRI Data

In functional magnetic resonance imaging (fMRI) data analysis, effective connectivity investigates the influence that brain regions exert on one another. Structural equation modeling (SEM) has been the main approach to examine effective connectivity. In this paper, we propose a method that, given a set of regions, performs partial correlation analysis. This method provides an approach to effective connectivity that is data driven, in the sense that it does not require any prior information regarding the anatomical or functional connections. To demonstrate the practical relevance of partial correlation analysis for effective connectivity investigation, we reanalyzed data previously published [Bullmore, Horwitz, Honey, Brammer, Williams, Sharma, 2000. How good is good enough in path analysis of fMRI data? NeuroImage 11, 289-301]. Specifically, we show that partial correlation analysis can serve several purposes. In a pre-processing step, it can hint at which effective connections are structuring the interactions and which have little influence on the pattern of connectivity. As a post-processing step, it can be used both as a simple and visual way to check the validity of SEM optimization algorithms and to show which assumptions made by the model are valid, and which ones should be further modified to better fit the data.