The effect of latent confounding processes on the estimation of the strength of casual influences in chain-type networks
Main Article Content
Abstract
Reliable recognition of casual interactions between processes is an issue particularly prevalent in the Neurosciences. When the structure of a network is not a priori known it is almost impossible to observe and measure all components of a system, and missing certain components could potentially lead to the inference of spurious interactions. The aim of this study is to demonstrate the effect of missing components of a network on the inferred strength of a spurious interaction. Our novel method uses vector autoregressive modelling and renormalised partial directed coherence to show how and why the inferred strength of causal interactions between processes changes when components in a network are missed. In cases where a latent confounder is influencing a network and consequently a spurious interaction appears, it is not possible to rely on estimates of the strength of this link as strength estimation methods are influenced by the noise of the latent confounder. Our novel approach demonstrates precisely how a latent confounder can affect the strength measure using analysis of vector autoregressive models. While it is possible to measure the strength of directed causal influences between processes the estimation of strength can be confounded if not all components of a system have been observed during measurement.
Article Details
The Medical Research Archives grants authors the right to publish and reproduce the unrevised contribution in whole or in part at any time and in any form for any scholarly non-commercial purpose with the condition that all publications of the contribution include a full citation to the journal as published by the Medical Research Archives.
References
Dahlhaus, R., Eichler, M. and Sandkühler, J. 1997. Identification of synaptic connections in neural ensembles by graphical models. J. Neurosci. Meth. 77, 93-107.
Eichler, M. 2005. A graphical approach for evaluating effective connectivity in neural systems. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 360, 953-967.
Elsegai, H., Shiells, H., Thiel, M. and Schelter, B. 2015. Network inference in the presence of latent confounders: The role of instantaneous causalities. J. Neurosci. Meth. 245, 91-106.
Granger, C.W.J. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424-438.
Karamzadeh, N., Medvedev, A., Azari, A., Gandjbakhche, A. and Najafizadeh, L. 2013. Capturing dynamic patterns of task-based functional connectivity with EEG. NeuroImage 66, 311-317.
Ramb, R., Eichler, M., Ing, A., Thiel, M., Weiller, C., Grebogi, C., Schwarzbauer, C., Timmer, J. and Schelter, B. 2013. The impact of latent confounders in directed network analysis in neuroscience. Phil. Trans. R. Soc. A. 371, 20110612.
Rubinov, M. and Sporns, O. 2010. Complex network measures of brain connec- tivity: Uses and interpretations. NeuroImage 52, 1059-1069.
Schad, S., Nawrath, J., Jachan, M., Henschel, K., Spindeler, L., Timmer, J. and Schelter, B. 2009. Approaches to the detection of direct directed interactions in neuronal networks. In Coordinated Activity in the Brain, eds. J.L.P. Velazquez and R. Wennberg, Volume 2, Springer, 43-64.
Schelter, B., Winterhalder, M., Eichler, M., Peifer, M., Hellwig, B., Guschlbauer, B., Lücking, C.H., Dahlhaus, R. and Timmer, J. 2006. Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Meth. 152, 210-219.
Schelter, B., Timmer, J. and Eichler, M. 2009. E Assessing the strength of directed influences among neural signals using renormalized partial directed coherence. J. Neurosci. Meth. 179, 121-30.
Schreiber, T. 2000. Measuring information transfer. Phys. Rev. Lett. 85, 461- 464.
Smirnov, D.A. and Bezruchko, B.P. 2003. Estimation of interaction strength and direction from short and noisy time series. Phys. Rev. E 68, 046209.
Sommerlade, L., Thiel, M., Platt, B., Plano, A., Riedel, G., Grebogi, C., Tim- mer, J. and Schelter, B. 2012. Inference of Granger causal time-dependent influences in noisy multivariate time series. J. Neurosci. Meth. 203, 173-185.