## 3 Results and Discussion
### Model Performance Parameters  
Model performance parameters are metrics that are extrapolated from the confusion matrix, providing a nuanced understanding of the model performance. Below are some key parameters computed using Python on the test data [38]. Accuracy: This metric represents the ratio of the total number of correct instances to the total number of instances. It can be calculated as follows. Figure 12: Classification report and confusion matrix for models: (**a**) RF, (**b**) LR, and (**c**) XGBoost. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **TP** & **FN** & **FP** & **TN** & **Negative Predictive Value** & **False-Negative Rate** & **False-Positive Rate** \\ \hline RF & 890 & 89 & 143 & 788 & 0.899 & 0.091 & 0.154 \\ LG & 809 & 170 & 213 & 718 & 0.809 & 0.174 & 0.229 \\ XGBoost & 877 & 102 & 152 & 779 & 0.884 & 0.104 & 0.163 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix elements and derived metrics for the RF, LG, and XGBoost models. \[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{ FN}} \tag{3}\]  
Precision: This metric signifies the ratio of correctly predicted positive observations to the total number of predicted positives. It is calculated as follows. \[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{4}\]  
Recall (Sensitivity): This metric represents the proportion of accurately identified positive instances relative to the total number of instances within the actual classification. It is computed as follows. \[\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{5}\]  
Matthews Correlation Coefficient (MCC): The MCC serves as a more robust statistical measure that yields elevated scores exclusively when the predictive model demonstrates efficacy across all four categories within the confusion matrix (true positives, false negatives, true negatives, and false positives), while concurrently taking into account the proportionality of both positive and negative instances within the dataset. It functions as an indicator of the performance quality of binary classifiers. This metric integrates both true and false positives, as well as true and false negatives, and is widely acknowledged as a balanced metric applicable even in scenarios where the sizes of the classes diverge significantly. The MCC fundamentally represents a correlation coefficient that ranges from \(-1\) to \(+1\). A value of \(+1\) denotes a flawless prediction, while 0 indicates a prediction equivalent to random chance and \(-1\) signifies an inverse prediction. The formula for the MCC is articulated as follows. \[\text{MCC}=\frac{(\text{TP}\times\text{TN})-(\text{FP}\times\text{FN})}{\sqrt{ (\text{TP}+\text{FP})(\text{TP}+\text{FN})(\text{TN}+\text{FP})(\text{TN}+ \text{FN})}} \tag{6}\]  
where TP = true positives, TN = true negatives, FP = false positives, and FN = false negatives. Cohen's Kappa: Cohen's Kappa is a statistical measure employed to assess inter-rater reliability (as well as intra-rater reliability) concerning qualitative (categorical) items. It is typically regarded as a more resilient measure in comparison to a straightforward percentage agreement calculation, given that \(\kappa\) incorporates the potential for agreement arising due to chance. Nevertheless, it is important to acknowledge the ongoing discourse surrounding the application of Cohen's Kappa, attributable to its relative nature, which complicates the interpretation of its resultant values. The formula for Cohen's Kappa is as follows. \[\kappa=\frac{p_{o}-p_{e}}{1-p_{e}} \tag{7}\]  
where \(p_{o}\) is the relative observed agreement among raters (identical to accuracy) and \(p_{e}\) is the hypothetical probability of chance agreement. To evaluate the predictive performance of the models RF, XGBoost, and LR, we computed a comprehensive set of classification metrics beyond overall accuracy.