Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance

Abstract

We consider the question of evaluating causal relations among neurobiological signals. In particular, we study the relation between the directed transfer function (DTF) and the well-accepted Granger causality, and show that DTF can be interpreted within the framework of Granger causality. In addition, we propose a method to assess the significance of causality measures. Finally, we demonstrate the applications of these measures to simulated data and actual neurobiological recordings.

Multivariate Granger causality analysis of fMRI data

“…Methodologically, spectral methods have been shown to be more robust to deviations from the stationarity assumption [Granger, 1964]. It is to be noted that unlike previously reported studies Kaminski et al, 2001;Kus et al, 2004], we avoided normalizing DTF so as to allow direct comparison between the absolute values of the strengths of influence. Normalization of DTF with respect to inflows into any ROI as in Kus et al would make such a comparison untenable.…”

“…Analytical distributions of multivariate Granger causality are not established because they are said to have a highly nonlinear relationship with the time series data [Kaminski et al, 2001]. Therefore, to assess the significance of the Granger causality reflected by dDTF, we employed surrogate data [Kaminski et al, 2001;Kus et al, 2004;Theiler et al, 1992] to obtain an empirical null distribution.…”

“…Therefore, to assess the significance of the Granger causality reflected by dDTF, we employed surrogate data [Kaminski et al, 2001;Kus et al, 2004;Theiler et al, 1992] to obtain an empirical null distribution. The original time series was transformed into the frequency domain and their phase was randomized so as to be uniformly distributed over (2p, p) .…”

“…Simulations by Kus et al [2004] have shown that a complete set of observations from a process have to be used to obtain causal relationships between them and that pair-wise estimates may yield incorrect results. To date, multivariate measures of Granger causality have been largely limited to electrophysiological data Ding et al, 2000;Kaminski et al, 2001;Kus et al, 2004] although multivariate autoregressive models have been used to infer functional connectivity from fMRI data [Harrison et al, 2003]. We have previously presented preliminary forms of the study described here [Deshpande et al, 2006a,b].…”

Non-parametric directionality analysis – Extension for removal of a single common predictor and application to time series

“…The majority of approaches are parametric, which rely on estimating the parameters of a model to describe the patten of interactions between the observed signals, typically using autoregressive (AR) models (Granger, 1969;Geweke, 1982). Once the AR parameters have been estimated different metrics relating to directionality can be constructed directly as a function of the model parameters (Baccala et al, 2001;Kaminski et al, 2001;Chen et al, 2006;Schelter et al, 2006;Chicharro, 2012). A number of concerns have been raised regarding the validity of AR models to accurately capture the complex structure present in multivariate neural and other time series typically encountered in scientific problems (Gersch, 1972;Thomson and Chave, 1991;Lindsay and Rosenberg, 2011).…”