## 3 Results
Table 2 shows the Kruskal-Wallis tests' \(p\)-values across the Sham montages comparison (Anodal, AC, versus Cathodal, CC), for each TE response, within stimuli off (pre/post-stimulation) or during stimuli (1, 2, or 3 mA), in which none of them presented statistically different patterns within the observed group (limited to the sample size observed in this protocol study). It is noteworthy that Sham-AC shows an equivalent pattern to the Sham-CC. A theoretical GLMM was adopted to explain the Transfer Entropy dynamic through a combination of montages and intensity, the variables time and platform side (if the transfer information is from the Right-side or the Left-side to the other), and also considering that each participant shows a personal response (that is, as a latent effect). Moreover, this regression structure is explained with multiplicative error, then as a GLMM with Gamma distribution considering a logarithmic link, and the stochastic component is described by a Gamma model with scale parameter \(\
u\), observation of \(k\) participants in groups \(i\) -Montages- and \(j\) -Doses-, for \(k=\{1,\ldots,20\}\), \(i=\{\)\"Baseline\", \"Sham-Cathodal\", \"Sham-Anodal\", \"Cathodal\", \"Anodal\" and \(j=\{\)\"0 mA (Pre- or Post-Stimulation)\", \"1 mA\", \"2 mA\", \"3 mA\"\(\}\). That is,  
\[\text{Transfer entropy response (Y}_{ijk})\sim Gamma(y_{ijk}H_{ijk},\
u) \tag{2}\] \[\mu_{ijk}:=\mathbb{E}[Y_{ij}\mathbf{X}_{ij}]=\mathbf{e}^{X_{ij}\mathbf{\beta} +Z_{ijk}\mathbf{\gamma}_{k}}\] (3) \[\text{whereas }\mathbf{X}_{ij}\mathbf{\beta}=\beta_{1}^{(i)}\mathbf{Montage}+ \beta_{2}^{(j)}\mathbf{Dose}+\beta_{3}^{(ij)}\mathbf{Montage}*\mathbf{Dose}+\beta_{4}\mathbf{ Time}+\] (4) \[\beta_{5}\mathbf{Side}+\beta_{6}\mathbf{Time}*\mathbf{Side} \tag{5}\]  
in which \(\mathbf{X}_{ij}\) is the described array of known fixed effects explanatory variables, \(\beta\) is the p-dimensional vector of fixed effects coefficients, \(Z_{ijk}\) is the array of known personal random effects explanatory variables and \(\gamma_{k}\) is the q-dimensional vector of personal random effects (normally distributed with mean equal to zero). The GLMM brings the results related to montage, intensity, time, and side (complete table in Appendix A, and its Bayesian version, which also contains the effective sample size estimate in Appendix B). Fixing each intensity and observing the interaction among \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Stimuli Moment** & **Sham-Anodal** & **Sham-Cathodal** \\  & & **Median [Range]** & **Median [Range]** \\ \hline \multirow{3}{*}{Right \(\rightarrow\) Left} & PRE or POST (OFF) & 0.0397 [0.02, 0.10] & 0.0438 [0.02, 0.10] \\  & 1 mA (ON) & 0.0314 [0.01, 0.10] & 0.0429 [0.01, 0.13] \\  & 2 mA (ON) & 0.0433 [0.02, 0.12] & 0.052 [0.01, 0.10] \\  & 3 mA (ON) & 0.0373 [0.02, 0.10] & 0.0481 [0.01, 0.09] \\ \hline \multirow{3}{*}{Left \(\rightarrow\) Right} & PRE or POST (OFF) & 0.0266 [0.01, 0.12] & 0.0396 [0.01, 0.12] \\  & 1 mA (ON) & 0.0225 [0.01, 0.13] & 0.0393 [0.00, 0.16] \\  & 2 mA (ON) & 0.0205 [0.01, 0.15] & 0.0667 [0.01, 0.13] \\  & 3 mA (ON) & 0.0206 [0.01, 0.11] & 0.0469 [0.00, 0.11] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive comparison between Sham-Anodal and Sham-Cathodal. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{_p-Value_} \\ \hline
**Stimuli Moment** & **Left-Side** & **Right-Side** \\ \hline PRE or POST (OFF) & 0.529 & 0.505 \\
1 mA (ON) & 0.791 & 0.375 \\
2 mA (ON) & 0.099 & 0.214 \\
3 mA (ON) & 0.255 & 0.408 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Kruskal–Wallis tests considering each force place (information flux comes from the Left-side, Left \(\rightarrow\) Right, or Right-side, Right \(\rightarrow\) Left) across the difference between Sham-Anodal versus Sham-Cathodal stimulation observation per period. montages, cathodal condition up to 2 mA presented statistically different against Sham (Figure 6). The decrease in the entropy on the left platform was influenced by the flow of information from the right side.