# Machine Learning for Evaluating Hospital Mobility: An Italian Case Study
## 4 Experimental Results and Discussions
### Specific Feature Contributions by Target Class in the Hospital Mobility Model  
We adopted SHAP (SHapley Additive exPlanations) for the fair interpretation of variables in our logistic regression model, crucial for informed decisions in healthcare. This technique, which assigns an impact value to each feature, has been applied in studies demonstrating its value in the analysis of complex models [31]. Figure 9 provides a visual representation of how different features influence the classification of patients into LOW, MEDIUM, and HIGH mobility categories through SHAP analysis. The gray boxes highlight the base probability values and the predictions modified by SHAP values. The probability scale is indicated along the sidebar, with SHAP values shown in white and numerical feature values in black. Red ribbons indicate an increase in the probability of belonging to a particular mobility class, while blue ribbons indicate a decrease. The graphical representation was facilitated by the Explain Prediction widget, displayed in the green box in Figure 2. For the LOW target class, which identifies patients with low mobility, meaning those less inclined to travel long distances for hospital care, SHAP value analysis reveals which features weigh most heavily in their decision to choose a hospital. A lower availability of beds (BEDS), indicated by a SHAP value of 0.046 (VALUE of \(-0.8\)), correlates with an increased probability that patients will turn to closer facilities, suggesting a direct link between resource availability and the decision not to travel for medical care. The number of departments (DEPARTMENTS) with a SHAP value of 0.042 (VALUE of \(-0.68\)) and hospital staff (HOSPITAL STAFF) with a SHAP value of 0.031 (VALUE of \(-0.54\)) demonstrate how diversified healthcare offerings and a broad hospital group can be reassuring elements for patients, who may then choose closer hospitals rather than exploring farther options. Mortality rate (DEATHS) emerged as the most decisive factor, with a SHAP value of 0.145 (VALUE of \(-0.63\)), indicating that higher mortality rates significantly dissuade patients from choosing certain facilities. This highlights how the perception of quality of care is a critical factor affecting healthcare mobility. Finally, nursing care, measured by the number of nurses (NURSES), with a SHAP value of 0.056 (VALUE of \(-0.57\)), confirms that good nursing care is valued by patients, who tend to prefer nearby facilities perceived as better equipped to provide immediate and quality care. The model starts with a base probability of 65%, and considering the set of analyzed features, it predicts a probability of 95% that patients will opt for low mobility. In the MEDIUM target class, the model highlights how certain hospital characteristics negatively influence patient mobility, pushing the base probability of 0.22 towards a lower predictive value of 0.05. The negative SHAP value for departments (DEPARTMENTS) of \(-0.032\) (VALUE of \(-0.68\)) suggests that a wide range of specializations within the hospital reduces the need for patients to travel average distances, as their needs can be met locally. Similarly, a high perception of hospital staff quality (HOSPITAL STAFF), indicated by a SHAP value of \(-0.023\) (VALUE of \(-0.54\)), and adequate nursing staffing (NURSES), with a SHAP value of \(-0.059\) (VALUE of \(-0.57\)), reinforce the trend of patients preferring nearby hospitals. These characteristics, indicating comprehensive and quality hospital care, thus seem to discourage patients from seeking care at farther facilities. The strongest signal encouraging patients to stay nearby is given by the mortality rate (DEATHS), with a significant SHAP value of \(-0.15\) (VALUE of \(-0.63\)). A lower mortality rate within a  
Figure 9: SHAP analysis for predicting mobility class. hospital is a clear indicator of care quality and safety, which appears to be a decisive factor in limiting patient mobility.