A lack of statistical pitfalls in the comparison of multivariate causality measures for effective causality

In a 2011 paper, Wu et al. Comp. Biol. Med. 41 (2011) 1132-1141, compared the performance of several standard causal connectivity measures including Granger Causality (GC) using both simulated data sets and real magnetoencephalography data. Parameters for the causal connectivity measures were obtained using the Dynamic Autoregressive Neuromagnetic Causal Imaging (DANCI) algorithm. In a letter, Dr. Florin and Dr. Pfeifer Comp. Biol. Med. 43 (2013) 131-134, outline four shortcomings of Wu et al. Comp. Biol. Med. 41 (2011) 1132-1141, study. We provide counterarguments for the appropriateness of our approach and demonstrate how, despite any shortcomings, the Wu et al. Comp. Biol. Med. 41 (2011) 1132-1141 study provides an important and valid analysis of these various causal connectivity methods. In particular, none of the findings are consistent with limitation of the dynamic autoregressive neuromagnetic causal imaging (DANCI) algorithm and/or Granger causality (GC) method described by Frye and Wu Comp. Biol. Med. 41 (2011) 1118-1131. In fact, many of the limitations raised by Florin and Dr. Dr. Pfeifer illustrate the significant advantage of the DANCI algorithm and GC method for the analysis of causal connectivity.