Matching structural, effective, and functional connectivity: a comparison between structural equation modeling and ancestral graphs

In this study, we examined the accuracy of ancestral graphs (AGs) to study effective connectivity in the brain. Unlike most other methods that estimate effective connectivity, an AG is able to explicitly model missing brain regions in a network model. We compared AGs with the conventional structural equation models (SEM). We used both methods to estimate connection strengths between six regions of interest of the visual cortex based on functional magnetic resonance imaging data of a motion perception task. In order to examine which method is more accurate to estimate effective connectivity, we compared the connection strengths of the AG and SEM models with connection probabilities resulting from probabilistic tractography obtained from diffusion tensor images. This was done by correlating the connection strengths of the best fitting AG and SEM models with the connection probabilities of the probabilistic tractography models. We show that, in general, AGs result in more accurate models to estimate effective connectivity than SEM. The reason for this is that missing regions are taken into account when modeling with AG but not when modeling with SEM: AG can be used to explicitly test the assumption of missing regions. If the set of regions is complete, SEM and AG perform about equally well.