How does multicollinearity affect brain connectivity estimation? A simulation study based on penalized regression technique

Methods based on the use of multivariate autoregressive modelling (MVAR) have proved to be an accurate and flexible tool for the estimation of brain connectivity. However, the multivariate approach, implies that the number of parameters to be estimated, increases quadratically with the number of time series included in the model. This can often lead to an undetermined problem and to the condition known as multicollinearity. The aim of this paper is to introduce and test an approach on EEG surrogate signals, based on penalized regression technique to broaden the estimation of brain connectivity to those conditions in which current methods fail due to the lack of enough data points. We tested the performances of the least absolute shrinkage and selection operator (LASSO) in comparison with the classical approach based on ordinary least square regression (OLS) for the parameters estimation combined with asymptotic statistics (AS) for the assessment procedure, by means of a simulation study implementing different ground-truth networks, under different levels of data points and different values of signal to noise ratio. Simulation results showed that the approach based on LASSO provides better performances, in term of accuracy of the parameters estimation and false positives/false negatives rates, in all conditions related to a low data points and low SNR. This work paves the way to estimate and validate estimated patterns at single trial level or when short time data segments are available