## 4 Results
### Models and Statistical Validation
Figure 6 shows a comparison of the best-adjusted ANN models. The optimal number of neurons in the hidden layer and the regularization parameter value for each of the models are shown in Table 6. The table shows that all sets reach similar combined performance values (above 83%), except for SET-4, which shows a decrease. The model with the best performance is SET-3 since it has the highest AUC value (95.21%) and the lowest error rate (10.27%). Under the combined performance criterion, the model with the best performance is also SET-3 since it has the highest value (85.43%). Both criteria are coincident, suggesting that it is a robust and reliable model. To ensure the robustness of this model, the loss function was analyzed in comparison to the validation loss (Figure 7). Both metrics decrease as the size of the training set increases. They converge and reach a low value, indicating high model robustness and generalization capability. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predictor** & **Average AUC (\%)** & **Average Error Rate (\%)** & **Combined Performance (\%)** \\ \hline SET-1 & 92.20 & 14.86 & 78.50 \\ SET-2 & 94.19 & 12.74 & 82.19 \\ SET-3 & 94.03 & 13.27 & 81.56 \\ SET-4 & 87.97 & 20.76 & 69.71 \\ SET-5 & 94.16 & 12.91 & 82.00 \\ SET-6 & 94.02 & 13.08 & 81.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Combined performance value for each LG model built from each set of developed predictors. Figure 4: Box-plot showing performance comparison of LG models for each predictor set with training data, comparing the AUC and error rate of each, to select the best sub-model. Furthermore, the data dispersion does not seem to be large enough to significantly affect the model selection, as there is no great variability in the values for each metric of the analyzed models. This suggests that the results are consistent and are not significantly influenced by outliers or extreme values in the data. Additionally, the average AUC and error values for each model are quite stable and remain within a narrow range of values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Predictor** & **Hidden** & **L2 Penalty** & **Average** & **Average Error** & **Combined** \\  & **Nodes** & **Rate** & **AUC (\%)** & **Rate (\%)** & **Performance (\%)** \\ \hline SET-1 & 5 & 0.10 & 94.42 & 11.67 & 83.39 \\ SET-2 & 17 & 0.10 & 94.87 & 10.93 & 84.49 \\ SET-3 & 9 & 0.10 & 95.21 & 10.27 & 85.43 \\ SET-4 & 10 & 0.01 & 91.27 & 15.80 & 76.85 \\ SET-5 & 13 & 0.10 & 95.00 & 10.98 & 84.57 \\ SET-6 & 10 & 0.10 & 94.81 & 11.01 & 84.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimal hyperparameter values for each of the average ANN models created from the training data. Figure 5: Box-plot showing performance comparison of RF models for each predictor set with training data, comparing the AUC and error rate of each, to select the best submodel. The optimal number of variables selected for each partition of each tree was 3 for the model that uses SET-1 as predictor variables, 6 for the model with all variables, and 4 for the remaining sets. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predictor** & **Average AUC (\%)** & **Average Error Rate (\%)** & **Combined Performance (\%)** \\ \hline SET-1 & 95.08 & 11.30 & 84.33 \\ SET-2 & 95.11 & 11.10 & 84.56 \\ SET-3 & 95.31 & 10.89 & 84.94 \\ SET-4 & 92.57 & 14.24 & 79.39 \\ SET-5 & 95.25 & 10.97 & 84.80 \\ SET-6 & 95.08 & 11.16 & 84.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Combined performance value for each RF model built from each set of developed predictors. of outliers like SET-5. Overall, both models present similar distributions in terms of AUC, although SET-5 seems to have a higher concentration of data around the median. Regarding the error, both models present a left-skewed distribution and the presence of outliers. Based on this information, it is difficult to decide with certainty which of the two models is better. Considering only the performance in terms of AUC and error, both models present similar results.