## 3 Results
### Cross-Validation of Training Data  
This section presents results on model training validation using both the original and augmented data. Table 11 presents the mean scores from the 5-fold stratified cross-validation performed on both datasets. For each model, the average macro and weighted F1 scores are presented for the original imbalanced data, while only the macro average is presented for the balanced data. Corresponding standard deviations are also reported to provide information on performance variability and model stability.  
The results generated from the original data show that the GBM model reported the highest average F1 scores of 0.8730 (\(\pm\)0.0044) for weighted and 0.8489 (\(\pm\)0.0051) for macro. The mean scores of the XGB and RF models were marginally lower. The XGB model reported a weighted F1 score of 0.8687 (\(\pm\)0.0063) and a macro F1 score of 0.8445 (\(\pm\)0.0070), while the RF model reported 0.8592 (\(\pm\)0.0081) for weighted F1 score and 0.8299 (\(\pm\)0.0098) for macro F1 score. The ANN model, on the original data, reported relatively high average weighted (0.8440 (\(\pm\)0.0041)) and macro (0.8136 (\(\pm\)0.0049)) F1 scores. The results from the 5-fold cross-validation are presented in boxplots in Figure 7.  
The ANN model results were lower than those reported by the three ensemble methods but higher than those reported by the LR and SVM models. The average F1 scores reported by the SVM were below 80%, with a weighted F1 score of 0.6950 (\(\pm\)0.0351) and a macro F1 score of 0.6646 (\(\pm\)0.0348). Overall, ensemble tree classifiers (GBM, XGB, RF) yielded better classification performance compared to the other models during cross-validation on the original data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Birth Season**} & \multicolumn{2}{c}{**DEFAULTULTERS**} & \multicolumn{2}{c}{**NON-DEFAULTULTERS**} & \multirow{2}{*}{\(p\)**-Value**} \\  & **(_n_ = 9544)** & & & **(_n_ = 4180)** & \\ \hline  & \(n\) & \% & \(n\) & \% & \\ \hline Major rainy season & 3553 & 37.23 & 1801 & 43.09 & \\ Minor rainy season & 1634 & 17.12 & 670 & 16.03 & \textless{}0.001 \\ Dry season & 3569 & 37.40 & 1351 & 32.32 & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Analysis of birth season by defaulters and non-defaulters.  
The results from the augmented data (Table 12) showed comparatively improved F1 scores across all models.  
The SVM reported an increase in macro F1 score from 0.6646 \(\pm\) 0.0348 to 0.7516 \(\pm\) 0.0445. Similarly, the ANN and XGB models showed improvements in F1 score post augmentation, with the ANN's score increasing from 0.8136 \(\pm\) 0.0049 to 0.9043 \(\pm\) 0.0057 and XGB's score increasing from 0.8515 \(\pm\) 0.0058 to 0.9035 \(\pm\) 0.0230. The scores of high-performing RF and GBM models also increased with data augmentation. The RF model's macro F1 score increased from 0.8254 \(\pm\) 0.0085 to 0.8881 \(\pm\) 0.0060, while the GBM model's score rose from 0.8491 \(\pm\) 0.0090 to 0.8805 \(\pm\) 0.0121. Thus, after augmentation, the RF model reported the highest performance. Cross-validation results from the augmented data are presented as boxplots in Figure 8.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Model**} & **Average F1 Score** \\ \cline{2-3}  & **Macro (Augmented)** \\ \hline LR & 0.8458 \(\pm\) 0.0039 \\ SVM & 0.7516 \(\pm\) 0.0445 \\ RF & 0.8881 \(\pm\) 0.0060 \\ GBM & 0.8805 \(\pm\) 0.0121 \\ XGB & 0.9035 \(\pm\) 0.0230 \\ ANN & 0.9043 \(\pm\) 0.0057 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Average F1 score for 5-fold cross-validation on original and augmented datasets.  
Figure 7: Boxplots for 5-fold cross-validation on original dataset.