Asymmetrical Functional Connectivity Z-scores in CONN-Toolbox Using Multivariate Regression Analysis?

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1

I am requesting some insight into how multivariate regression analyses are implemented in CONN.

Looking at the z-score matrices of a bivariate correlation analysis and a multivariate regression analysis on the same subjects results in asymmetrical between-network z-scores for multivariate regression, and symmetrical z-scores for bivariate correlation. For clarification, I am looking at the functional connectivity between the DMN and visual network, and within both networks. Looking at the z-score matrix from the multivariate regression analysis, the scores between and within networks are asymmetrical (so the z-score from DMN-VN is not equivalent to the z-score from VN-DMN).

I was under the impression that the correlations would be bi-directional no matter the analysis run, so I am concerned that the asymmetries in the z-scores that appear when running a multivariate regression are the result of an error. I found elsewhere that uni-directional (asymmetrical) correlations have their perks (Asymmetric high-order anatomical brain connectivity sculpts effective connectivity - PMC), but I cannot figure out if CONN is actually computing uni-directional correlations for the multivariate regression analysis, since I cannot find any information about this in the documentation.

Are these asymmetries to be expected or are they the result of an error in the analysis?

2

Asymmetries are expected. Multivariate analyses between a set of ROIs (ROI_i with i=1…N) compute the association between every pair of ROIs (ROI_i and ROI_j) while controlling for all other N-2 ROIs (ROI_k, with k≠i,j). When selecting in CONN the “multivariate regression” output measure, the resulting connectivity matrices will contain the regression coefficients estimated from these models, which will be asymmetric, and when selecting “multivariate correlation” the connectivity matrices will contain Fisher-transformed semipartial correlation coefficients estimated from the same models, which are also asymmetric. For more details see https://conn-toolbox.org/fmri-methods/connectivity-measures/roi-to-roi

Best
Alfonso