## 4 Results  
This section describes the results from our experiments for evaluating the effectiveness of the different ML approaches using the BiLSTM neural network on the three educational datasets or entities presented in Section 3.1. Our main goal was to understand how performance varied for each approach and reveal their main advantages and drawbacks. We followed the same methodology for all experiments with the three entities' datasets  
Figure 12: BiLSTM prediction model. and the different approaches. We executed the deep learning model in a 10-fold cross-validation to ensure the reliability of our results through training and testing with different partitions of the datasets in each iteration. This allowed us to understand how well each method performed overall and its ability to handle new and unexpected data. As a baseline for comparison, we considered the individual or local model trained and tested at the same entity. To evaluate the predictive performance of our models, taking into account the imbalance in the data and ensuring a robust assessment of effectiveness in predicting student dropout, we used the two following metrics:  
1. AUC-ROC: The area under the ROC curve is one of the most important metrics used to represent the expected performance of a classifier based on the area under the receiver operating characteristic curve (AUC). The AUC is formally defined as the result of applying a prediction threshold, denoted as in Equation (2), \[AUC(f(\theta))=\int_{0}^{1}TPR(FPR(f_{i}(\theta)))d\iota\] (2) where \(\iota\) represents the prediction threshold applied to model predictions, and TPR and FPR represent the true positive rate and false positive rates, respectively. AUC scores are limited to a range of zero to one, with a random predictor achieving an AUC of 0.5. Given the unbalanced distribution of the data, we used the AUC-ROC to assess the overall predictive accuracy of our models in accurately capturing dropout patterns. 2. \(\Delta\)AUC: The increment in AUC-ROC is defined to measure changes in predictive performance as shown in Equation (3): \[\Delta AUC\big{(}T,\ T^{\prime}\big{)}=AUC(T)-AUC\big{(}T^{\prime}\big{)}\] (3) where AUC(T\({}^{\prime}\)) refers to the AUC of an individual model, and AUC(T) refers to a model trained with another approach. This allowed us to compare, for example, how AUC values were affected by different approaches. If \(\Delta\)AUC was close to zero, we could conclude that the model performs approximately the same as individual models, but if it was positive or negative, the model performed better or worse, respectively, in context T relative to T\({}^{\prime}\). Next, we show the results of executing 10 cross-validations of the individual, centralized, transfer (direct, repurposed, voting, and stacked) and federated learning approaches. We evaluated the performance of each approach separately for each target entity's dataset. This also allowed us to demonstrate how model performance varied based on the size of the target datasets. Figures 13-15 show the results for each destination entity in our study, demonstrating the AUC (area under the curve) and \(\Delta\)AUC (increment of AUC) metrics. Our visual representation includes bar charts illustrating the average AUC achieved by each approach. Box plots are also used to display the distribution of \(\Delta\)AUC values, centered around zero, allowing a clearer visualization of improvements or declines. The left side of Figure 13 shows the results of the different approaches in terms of AUC when the first dataset (in our case the biggest) was the target. In that case, the baseline was its own individual/local model trained on its own data giving a mean value for the AUC of 0.8166 \(\pm\) 0.0042. The AUC values ranged between 0.819 and 0.746 which were the lowest of the three target datasets. The centralized model produced a similar but lower performance than the baseline, with an AUC of 0.8109 \(\pm\) 0.0042.