Fundamental problems in Granger causality analysis of neuroscience data

Abstract

Granger causality methods analyze the flow of information between time series. The Geweke measure of Granger causality (GG-causality) has been widely applied in neuroscience because its frequency-domain and conditional forms appear well-suited to highly-multivariate oscillatory data. In this work, I analyze the statistical and structural properties of GG-causality in the context of neuroscience data analysis. 1. I analyze simulated examples and derive analytical expressions to demonstrate how computational problems arise in current methods of estimating conditional GG-causality. I show that the use of separate full and reduced models in the computation leads to either large biases or large uncertainties in the causality estimates, and high sensitivity to uncertainties in model parameter estimates, producing spurious peaks, valleys, and even negative values in the frequency domain. 2. I formulate a method of correctly computing GG-causality that resolves the above computational problems. 3. I analyze how generative system properties and frequency structure map into GG-causality to demonstrate deeper conceptual pitfalls: (a) I use simulated examples and derive analytical expressions to show that GG-causality is independent of the receiver dynamics, particularly the magnitude of response, which is counter-intuitive to physical notions of causality. (b) Overall, GG-causality combines transmitter and channel dynamics in a way that cannot be disentangled without evaluating the component dynamics of the full model estimate. 4. I discuss relevant concepts from causality analyses in other fields to better place causality analysis in a modeling and system identification framework. The computational uncertainties in GG-causality estimates make the interpretation of frequency-domain structure highly problematic. Even if these computational issues are overcome, correct interpretation of the GG-causality values is still challenging and could be easily misinterpreted without careful consideration of the component dynamics of the full model estimate. Through this work, I provide conceptual clarification of GG-causality and place it in the broader framework of modeling and system analysis, which may enable investigators to better assess the utility and interpretation of such methods.