## 3 Methodology
### Model Comparison and Evaluation  
In this section, we compare the performance of the eight machine learning algorithms introduced earlier based on key evaluation metrics commonly used in assessing classification models. These metrics include accuracy, precision, recall, F1 score, and area under the receiver operating characteristic curve (AUC-ROC). By comparing these metrics, our aim is to identify the most effective model for predicting student dropout rates.  
Definitions of Notations:  
True Positive (TP): The number of instances correctly predicted as positive.  
True Negative (TN): The number of instances correctly predicted as negative.  
False Positive (FP): The number of instances incorrectly predicted as positive.  
False Negative (FN): The number of instances incorrectly predicted as negative.  
Metrics:  
Accuracy: The ratio of correctly predicted instances to the total instances.  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\]Precision: The ratio of correctly predicted positive observations to the total predicted positives.  
\[Precision=\frac{TP}{TP+FP}\]  
Recall: The ratio of correctly predicted positive observations to all observations in the actual class.  
\[Recall=\frac{TP}{TP+FN}\]  
F1 score: Weighted average of precision and recall.  
\[FI-Score=2\frac{Precision*Recall}{Precision+Recall}\]  
AUC-ROC: Area under the ROC, which plots the true positive rate (TPR) against the false positive rate (FPR).  
The performance of each model was evaluated using these metrics on a test dataset. The model with the highest scores across these metrics is considered to be the best for predicting student dropout rates.  
Model evaluation is a crucial step in assessing the performance of machine learning models. This process involves testing the models on a separate validation dataset that was not utilized during the training phase. The evaluation process includes specific steps to ensure clarity and repeatability:  
Train/Test Split: The dataset was divided into 80% training data and 20% testing data to maintain consistency and transparency in the evaluation process.  
Cross-validation: In this study, K-fold cross-validation (k = 10) was adopted to enhance robustness and generalizability of the model.  
Evaluation Metrics: We calculate the evaluation metrics, such as accuracy, precision, recall, F1 score, and AUC-ROC, for each model, as described in the Model Comparison subsection.  
Confusion Matrix: We ensured a detailed breakdown of the model's predictions by generating a confusion matrix.  
ROC: The ROC for each model to was plotted visualize its performance across various threshold values.  
Hyperparameter Tuning: The hyperparameters of each model were tuned using methods like grid search or random search to discover the optimal parameters that maximize performance.  
By specifying parameters for model evaluation, such as those outlined above, this study can be repeated independently or expanded upon in future research. This process is vital for enhancing the repeatability and validity of the study results. The model evaluation process assists in identifying the strengths and weaknesses of individual algorithms, aiding in the selection of the most suitable model for predicting student dropout rates using data from the NEAS 2022 dataset, as summarized in Figure 1.