Investigating brain connectivity using mixed effects vector autoregressive models

We propose a mixed-effects vector auto-regressive (ME-VAR) model for studying brain effective connectivity. One common approach to investigating inter-regional associations in brain activity is the multivariate auto-regressive (VAR) model. The standard VAR model unrealistically assumes the connectivity structure to be identical across all participants in a study and therefore, could yield misleading results. The ME-VAR model overcomes this limitation by incorporating a participant-specific connectivity structure. In addition, the ME-VAR models can capture connectivity differences across experimental conditions and patient groups. The ME-VAR model directly decomposes the connectivity matrices into (i.) the condition-specific connectivity matrix, which is shared by all participants in the study (fixed effect) and (ii.) a participant-specific component (random effect) which accounts for between-subject variation in connectivity. An advantage of our approach is that it permits the use of both theoretical results on mixed effects models and existing statistical software when fitting the model. Another advantage of the proposed approach is that it provides improved estimates of the within-subject coefficients (the random effects) by pooling information across subjects in a single-stage rather than the usual two-stage approach. We illustrate the ME-VAR model on a functional MRI data set obtained to investigate brain connectivity in the prefrontal, pre-motor and parietal cortices while humans performed a motor-related, decision-making and action selection task.