A principled multivariate intersubject analysis of generalized partial directed coherence with Dirichlet regression:...

Background Generalized Partial Directed Coherence (GPDC) is a multivariate measure of predictability between functional timeseries defined in the frequency domain. However, analysis has often been constrained by its compositional nature. Specifically, the squared GPDC from a node region to all nodes in any given frequency must sum to one. New method When analyzing GPDC spectra, it is imperative to consider that squared GPDC from a source timeseries sums to one over its target timeseries. Dirichlet Regression allows the modeling of compositional data and, therefore, becomes a principled choice for the multivariate analysis of GPDC on arbitrary subject-level variables. Results Eleven resting-state fMRI connections underwent age-related alterations, with two decreases in squared GPDC from a region to itself in two frequencies, signaling increased integration with the rest, and nine increases in squared GPDC, one involving different regions. All frequencies had at least one alteration due to age. Comparison with existing method(s) Our methodology identifies alterations in GPDC in more connections than a naïve approach based on linear regression and centered log-ratio analysis. We also studied alternative connectivity indices between the same ROIs, uncovering no effect of age on the time-domain predictive-causality metrics for any connection, while for Pearson correlation five connections displayed significant effects of age, with parallels to the results pertaining to GPDC. Conclusions Dirichlet Regression allows the study of continuous or discrete variables as predictors for the analysis of GPDC, enabling a wider adoption of this measure of connectivity.