## 3 Results  
The GBM model was trained using the training set and was subsequently used to predict the \"Disposition\" of patients, represented as a binary variable (0 for \"HOME\", 1 for \"ADMITTED\"), in both the training and testing sets. We evaluated the model performance based on several metrics: Accuracy, Precision, Recall, F1 Score, and Area Under the Receiver Operating Characteristic Curve (AUC). On the training set, the model achieved an accuracy of 0.733, precision of 0.702, recall of 0.636, F1 score of 0.668, and AUC score of 0.720. The model's performance on the testing set was slightly lower but comparable, with an accuracy of 0.729, precision of 0.694, recall of 0.629, F1 score of 0.660, and AUC score of 0.715. The similar performance on both the training and testing sets suggests that our model was able to generalize well to unseen data and did not suffer from overfitting. As demonstrated by the AUC scores in Figure 2, our model's ability to distinguish between patients who were sent home and those who were admitted was fairly good. This indicates the model's potential utility in a real-world clinical setting. As a result of our methodology, we generated SHAP values and then illustrated them using SHAP summary and dependence plots. The summary plot gives an overview of the importance and impacts of features across all instances in the test dataset. It ranks the features by the sum of SHAP value magnitudes over all samples and uses SHAP values to show the distribution of the impacts each feature has on the model output. From the summary plot (Figure 3), it is clear that not all features contribute equally to the predictive power of the model. Certain features have a higher impact, which can be identified by their positions in the plot and by the color which indicates the feature value. This kind of plot provides a holistic view of feature importance and how each feature's value affects the output. Figure 2: Receiver Operating Characteristic (ROC) curve of the GBM model on the test set. The AUC score is 0.715, indicating good predictive performance. The SHAP summary plot, depicted in Figure 3, provides a holistic view of feature importance and the effects of feature values on the model predictions. The \(y\)-axis lists the features, and the \(x\)-axis quantifies the SHAP value. Each dot corresponds to a Shapley value for a feature and an instance. The features are ranked by importance from top to bottom, determined by the sum of SHAP value magnitudes over all samples. It is clear that \"Acuity\", \"Hours\", and \"Age\" are the top three influential factors in the model's decision-making process. The colors represent the feature value (red high, blue low). \"Acuity\" appears to be the most impactful feature. High \"Acuity\" values (red points) are associated with a positive SHAP value, indicating that high acuity levels increase the likelihood of the positive class. Conversely, low acuity levels decrease this likelihood. The \"Hours\" feature exhibits a mixed impact. Both high and low \"Hours\" values are found on either side of the SHAP value spectrum, indicating its complex relationship with the model's output. Lastly, the \"Age\" feature predominantly exhibits positive SHAP values, suggesting that an increase in \"Age\" generally contributes to a higher likelihood of the positive class. The insights from the SHAP summary plot, thus, provide an intuitive understanding of the model's behavior. They align with the expectations and prior knowledge in the healthcare context. Dependence plots were created for the features \"Acuity\", \"Hours\", and \"Age\". These were chosen because they were among the top features identified in the summary plot and their interaction effects with the model prediction are of particular interest in the scope of this study. The SHAP dependence plots (Figures 4-6) show the marginal effect one or two features have on the predicted outcome of a machine learning model. The color represents a third feature that may potentially interact with the \(x\)-axis feature.