Assessing Assumptions of Multivariate Linear Regression Framework implemented for Directionality Analysis of fMRI

Directionality analysis of time-series, recorded from task-activated regions-of-interest (ROIs) during functional Magnetic Resonance Imaging (fMRI), has helped in gaining insights of complex human behavior and human brain functioning. The most widely used standard method of Granger Causality for evaluating directionality employ linear regression modeling of temporal processes. Such a parameter-driven approach rests on various underlying assumptions about the data. The short-comings can arise when misleading conclusions are reached after exploration of data for which the assumptions are getting violated. In this study, we assess assumptions of Multivariate Autoregressive (MAR) framework which is employed for evaluating directionality among fMRI time-series recorded during a Sensory-Motor (SM) task. The fMRI timeseries here is an averaged time-series from a user-defined ROI of multiple voxels. The "aim" is to establish a step-by-step procedure using statistical methods in conjunction with graphical methods to seek the validity of MAR models, specifically in the context of directionality analysis of fMRI data which has not been done previously to the best of our knowledge. Here, in our case of SM task (block design paradigm) there is violation of assumptions, indicating the inadequacy of MAR models to find directional interactions among different task-activated regions of brain.