Testing effective connectivity changes with structural equation modeling: what does a bad model tell us?

Structural equation modeling (SEM) is a statistical method that can assess changes in effective connectivity across tasks or between groups. In its initial application to neuroimaging data, anatomical connectivity provided the constraints to decompose interregional covariances to estimate effective connections. There have been concerns expressed, however, with the validity of interpreting effective connections for a model that does not adequately fit the data. We sought to address this concern by creating two population networks with different patterns of effective connectivity, extracting three samples sizes (N = 100, 60, 20), and then assessing whether the ability to detect effective connectivity differences depended on absolute model fit. Four scenarios were assessed: (1) elimination of a region showing no task differences; (2) elimination of connections with no task differences; (3) elimination of connections that carried task differences, but could be expressed through alternative indirect routes; (4) elimination of connections that carried task differences, and could not be expressed through indirect routes. We were able to detect task differences in all four cases, despite poor absolute model fit. In scenario 3, total effects captured the overall task differences even though the direct effect was no longer present. In scenario 4, task differences that were included in the model remained, but the missing effect was not expressed. In conclusion, it seems that when independent information (e.g., anatomical connectivity) is used to define the causal structure in SEM, inferences about task- or group-dependent changes are valid regardless of absolute model fit.